We study gossip algorithms for the fundamental rumor spreading problem, where the goal is to disseminate a rumor from a given source node to all nodes in an arbitrary (and unknown) graph. Gossip algorithms allow each node to call only one neighbor per round and are therefore highly message-efficient, with low per-node communication overhead per round. The state of the art works present fast gossip algorithms, however they typically leverage large-sized messages. This undermines the lightweight communication advantage of gossip, since even though only one neighbor is contacted per round, the message size can be linear in í µí±, the network size. Hence, a fundamental question is whether one can perform fast gossip using small messages. The main contribution of this paper is to answer the above question in the affirmative and present two gossip algorithms that achieve fast rumor spreading using messages of polylog 𝑛 size. Specifically , we show the following results: (1) We present a gossip algorithm for rumor spreading that runs in 𝑂(𝑐 log𝑛/Φ𝑐 ) rounds for every 𝑐 ⩾ 1, and Φ𝑐 is the weak conductance. Our algorithm's run time not only improves over the Censor-Hillel-Shachnai bound [SODA 2011; SICOMP 2012], but more significantly, it uses messages of small (polylog 𝑛) size, unlike the prior work that used messages of large (at least linear in 𝑛) size. Our bound in terms of weak conductance is essentially optimal. (2) We also present a gossip algorithm for rumor spreading that depends on the network diameter (and is independent of the graph's conductance), which runs in \tilde{𝑂}(𝐷 +√𝑛) rounds with high probability and uses small (polylog 𝑛 size) messages. Our bound is a significant improvement over the gossip algorithm of \tilde{𝑂}(√𝑛𝐷) due to Ghaffari and Kuhn [DISC 2018], which also uses small-sized messages. We note that our algorithm (unlike that of Ghaffari and Kuhn) is optimal for when 𝐷 = Ω(√𝑛). Furthermore, our gossip algorithm can be modified to output a minimum spanning tree (MST) in the same number of rounds, which is essentially round-optimal (even for non-gossip algorithms). Our gossip algorithms use graph sketches [Ahn, Guha, McGregor, SODA 2012] in a novel way to overcome communication bottlenecks and achieve small communication overhead with small message sizes.

This talk will trace the interesting (hi)story behind the 2026 Dijkstra Prize work, “Distributed Verification and Hardness of Distributed Approximation” [STOC 2011, SICOMP 2012], by Das Sarma, Holzer, Kor, Korman, Nanongkai, Pandurangan, Peleg, and Wattenhofer. The talk will trace the origin of the Ω~(D+n) lower bound, first shown for the fundamental distributed Minimum Spanning Tree (MST) problem, to the discovery that the same bound applies to a wide variety of problems and settings known today. Along the way, it will talk about the impact of this work on distributed algorithms research over the last 15 years.

Random walks in distributed networks are useful primitives with numerous applications. In this paper, we focus on efficient distributed algorithms for performing random walks and their application to generating random spanning trees (RST) in arbitrary networks. The goal is to minimize the number of rounds required to output the positions of vertices in a random walk starting from a given source and to generate an RST in the standard CONGEST model.

Abstract Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best known (randomized) MIS algorithms have $$O(\log {n})$$ round complexity on general graphs [Luby, STOC 1986] (where n is the number of nodes), while the best known lower bound is $$\Omega (\sqrt{\log {n}/\log \log {n}})$$ [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the $$O(\log {n})$$ round complexity upper bound or showing stronger lower bounds have been longstanding open problems. Energy is a premium resource in various settings such as battery-powered wireless networks and sensor networks. The bulk of the energy is used by nodes when they are awake , i.e., when they are sending, receiving, and even just listening for messages. On the other hand, when a node is sleeping , it does not perform any communication and thus spends very little energy. Several recent works have addressed the problem of designing energy-efficient distributed algorithms for various fundamental problems. These algorithms operate by minimizing the number of rounds in which any node is awake , also called the (worst-case) awake complexity . An intriguing open question is whether one can design a distributed MIS algorithm that has significantly smaller awake complexity compared to existing algorithms. In particular, the question of obtaining a distributed MIS algorithm with $$o(\log n)$$ awake complexity was left open in [Chatterjee, Gmyr, Pandurangan, PODC 2020]. Our main contribution is to show that MIS can be computed in awake complexity that is exponentially better compared to the best known round complexity of $$O(\log n)$$ and also bypassing its fundamental $$\Omega (\sqrt{\log {n}/\log \log {n}})$$ round complexity lower bound exponentially. Specifically, we show that MIS can be computed by a randomized distributed (Monte Carlo) algorithm in $$O(\log \log {n} )$$ awake complexity with high probability (i.e., with probability at least $$1 - n^{-1}$$ ). This algorithm has a round complexity of $$O((\log ^7 n) \log \log n)$$ . We also show that we can improve the round complexity at the cost of a slight increase in awake complexity, by presenting a randomized distributed (Monte Carlo) algorithm for MIS that, with high probability, computes an MIS in $$O((\log \log {n})\log ^*n)$$ awake complexity and $$O((\log ^3 n) (\log \log n) \log ^*n)$$ round complexity. Our algorithms work in the $$\mathcal{CONGEST}$$ model where messages of size $$O(\log n)$$ bits can be sent per edge per round.

Maximal Independent Set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the radio networks model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm.

This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum communication gives an advantage for both problems by presenting quantum distributed algorithms that significantly outperform their respective classical counterparts under various network topologies.

Byzantine agreement is a fundamental problem in fault-tolerant distributed computing that has been studied intensively for the last four decades. Much of the research has focused on a static Byzantine adversary, where the adversary is constrained to choose the Byzantine nodes in advance of the protocol's execution. This work focuses on the harder case of an adaptive Byzantine adversary that can choose the Byzantine nodes adaptively based on the protocol's execution. While efficient O(log n)-round protocols (n is the total number of nodes) are known for the static adversary (Ben-Or, Goldwasser, Vaikuntanathan, FOCS 2006) tolerating up to t < n/(3 + ϵ) Byzantine nodes, [EQUATION] rounds is a well-known lower bound for adaptive adversary [Bar-Joseph and Ben-Or, PODC 1998]. The best-known protocol for adaptive adversary runs in O(t/log n) rounds [Chor and Coan, IEEE Trans. Soft. Engg., 1985].

Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the message complexity of distributed computing problems and its relationship (if any) with round complexity is still quite limited. To illustrate, for many fundamental distributed graph optimization problems such as (exact) diameter computation, All-Pairs Shortest Paths (APSP), Maximum Matching etc., while (near) round-optimal algorithms are known, message-optimal algorithms are hitherto unknown. More importantly, the existing round-optimal algorithms are not message-optimal. This raises two important questions: (1) Can we design message-optimal algorithms for these problems? (2) Can we give message-time tradeoffs for these problems in case the message-optimal algorithms are not round-optimal?

Byzantine agreement is a fundamental problem in fault-tolerant distributed networks that has been studied intensively for the last four decades. Most of these works designed protocols for complete networks. A key goal in Byzantine protocols is to tolerate as many Byzantine nodes as possible.

We address a fundamental problem in Peer-to-Peer (P2P) networks, namely, constructing and maintaining dynamic P2P overlay network topologies with essential properties such as connectivity, low diameter, and high expansion, that are resilient to continuous high churn and the presence of a large number of malicious (Byzantine) nodes. Our main goal is to construct and maintain a sparse (bounded degree) expander topology despite high churn and a large number of Byzantine nodes. Such an expander topology has logarithmic diameter, high expansion, and is robust to churn and the presence of a large number of bad nodes, and facilitates efficient and robust algorithms for fundamental problems in distributed computing, such as agreement, broadcasting, routing, etc.

The maximal independent set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the Radio Network model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm, which we want to minimize. We present new, more energy-efficient MIS algorithms in radio networks with arbitrary and unknown graph topology. We present algorithms for two popular variants of the radio model -- with collision detection (CD) and without collision detection (no-CD). Specifically, we obtain the following results: 1. CD model: We present a randomized distributed MIS algorithm with energy complexity $O(\log n)$, round complexity $O(\log^2 n)$, and failure probability $1 / poly(n)$, where $n$ is the network size. We show that our energy complexity is optimal by showing a matching $Ω(\log n)$ lower bound. 2. no-CD model: In the more challenging no-CD model, we present a randomized distributed MIS algorithm with energy complexity $O(\log^2n \log \log n)$, round complexity $O(\log^3 n \log Δ)$, and failure probability $1 / poly(n)$. The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of $O(\log^3 n)$ of the best known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.

We focus on designing Peer-to-Peer (P2P) networks that enable efficient communication. Over the last two decades, there has been substantial algorithmic research on distributed protocols for building P2P networks with various desirable properties such as high expansion, low diameter, and robustness to a large number of deletions. A key underlying theme in all of these works is to distributively build a random graph topology that guarantees the above properties. Moreover, the random connectivity topology is widely deployed in many P2P systems today, including those that implement blockchains and cryptocurrencies. However, a major drawback of using a random graph topology for a P2P network is that the random topology does not respect the underlying (Internet) communication topology. This creates a large propagation delay, which is a major communication bottleneck in modern P2P networks. In this paper, we work towards designing P2P networks that are communication-efficient (having small propagation delay) with provable guarantees. Our main contribution is an efficient, decentralized protocol, Close-Weaver, that transforms a random graph topology embedded in an underlying Euclidean space into a topology that also respects the underlying metric. We then present efficient point-to-point routing and broadcast protocols that achieve essentially optimal performance with respect to the underlying space.

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph G on n nodes and m edges, we can construct an overlay network that is a constant-degree expander in polylog rounds using only Õ(n) messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only Õ(n) messages, which is sublinear in m (even when m is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog rounds and o(m) messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model. In particular, a wide range of fundamental tasks such as broadcast, leader election, and minimum spanning tree (MST) construction can be accomplished in polylog rounds and Õ(n) message complexity in any graph.

The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results: 1) Cubic regime: Our first main contribution is showing essentially cubic, i.e., Ω̃(n³) lower bounds (where n is the number of nodes in the graph) on the message complexity of distributed exact computation of Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). Our lower bounds apply to any distributed algorithm that runs in polynomial number of rounds (a mild and necessary restriction). Our result is significant since, to the best of our knowledge, this are the first ω(m) (where m is the number of edges in the graph) message lower bound known for distributed computation of such classical graph optimization problems. Our bounds are essentially tight, as all these problems can be solved trivially using O(n³) messages in polynomial rounds. All these bounds hold in the standard CONGEST model of distributed computation in which messages are of O(log n) size. 2) Quadratic regime: In contrast, we show that if we allow approximate computation then Θ̃(n²) messages are both necessary and sufficient. Specifically, we show that Ω̃(n²) messages are required for constant-factor approximation algorithms for all four problems. For MaxM and MVC, these bounds hold for any constant-factor approximation, whereas for MDS and MaxIS they hold for any approximation factor better than some specific constants. These lower bounds hold even in the LOCAL model (in which messages can be arbitrarily large) and they even apply to algorithms that take arbitrarily many rounds. We show that our lower bounds are essentially tight, by showing that if we allow approximation to within an arbitrarily small constant factor, then all these problems can be solved using Õ(n²) messages even in the CONGEST model. 3) Linear regime: We complement the above lower bounds by showing distributed algorithms with Õ(n) message complexity that run in polylogarithmic rounds and give constant-factor approximations for all four problems on random graphs. These results imply that almost linear (in n) message complexity is achievable on almost all (connected) graphs of every edge density.

It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global problems such as broadcast, leader election, and spanning tree construction, under the KT₀ assumption. With this assumption, nodes have initial knowledge only of themselves, not their neighbors. In this case the time and message lower bounds are Ω(D) and Ω(m), respectively, where D is the diameter of the network and m is the number of edges, and there exist (even) deterministic algorithms that simultaneously match these bounds. On the other hand, under the KT₁ assumption, whereby each node has initial knowledge of itself and the identifiers of its neighbors, the situation is not clear. For the KT₁ CONGEST model (where messages are of small size), King, Kutten, and Thorup (KKT) showed that one can solve several fundamental global problems (with the notable exception of BFS tree construction) such as broadcast, leader election, and spanning tree construction with Õ(n) message complexity (n is the network size), which can be significantly smaller than m. Randomization is crucial in obtaining this result. While the message complexity of the KKT result is near-optimal, its time complexity is Õ(n) rounds, which is far from the standard lower bound of Ω(D). An important open question is whether one can achieve singular optimality for the above problems in the KT₁ CONGEST model, i.e., whether there exists an algorithm running in Õ(D) rounds and Õ(n) messages. Another important and related question is whether the fundamental BFS tree construction can be solved with Õ(n) messages (regardless of the number of rounds as long as it is polynomial in n) in KT₁. In this paper, we show that in the KT₁ LOCAL model (where message sizes are not restricted), singular optimality is achievable. Our main result is that all global problems, including BFS tree construction, can be solved in Õ(D) rounds and Õ(n) messages, where both bounds are optimal up to polylogarithmic factors. Moreover, we show that this can be achieved deterministically.

Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best known (randomized) MIS algorithms have O(log n) round complexity on general graphs [Luby, STOC 1986] (where n is the number of nodes), while the best known lower bound is [EQUATION] [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the O(log n) round complexity upper bound or showing stronger lower bounds have been longstanding open problems.

We present two distributed algorithms for the Byzantine counting problem, which is concerned with estimating the size of a network in the presence of a large number of Byzantine nodes.In an n-node network (n is unknown), our first algorithm, which is deterministic, finishes in O(log n) rounds and is time-optimal. This algorithm can tolerate up to O(n1−γ) arbitrarily (adversarially) placed Byzantine nodes for any arbitrarily small (but fixed) positive constant γ. It outputs a (fixed) constant factor estimate of log n that would be known to all but o(1) fraction of the good nodes. This algorithm works for any bounded degree expander network. However, this algorithms assumes that good nodes can send arbitrarily large-sized messages in a round.Our second algorithm is randomized and most good nodes send only small-sized messages.1This algorithm works in almost all d-regular graphs. It tolerates up to $B(n) = {n^{\frac{1}{2} - \xi }}$ (note that n and B(n) are unknown to the algorithm) arbitrarily (adversarially) placed Byzantine nodes, where ξ is any arbitrarily small (but fixed) positive constant. This algorithm takes O(B(n) log2n) rounds and outputs a constant factor estimate of log n with probability at least 1−o(1). The said estimate is known to most nodes, i.e., ≥ (1 − β)n nodes for any arbitrarily small (but fixed) positive constant β.To complement our algorithms, we also present an impossibility result that shows that it is impossible to estimate the network size with any reasonable approximation with any non-trivial probability of success if the network does not have sufficient vertex expansion.Both algorithms are the first such algorithms that solve Byzantine counting in sparse, bounded degree networks under very general assumptions. Both algorithms are fully local and need no global knowledge.Our algorithms can be used for the design of efficient distributed algorithms resilient against Byzantine failures, where the knowledge of the network size — a global parameter — may not be known a priori.

We present a simple algorithmic framework for designing efficient distributed algorithms for the fundamental symmetry breaking problem of Maximal Independent Set (MIS) in the sleeping model [Chatterjee et al, PODC 2020]. In the sleeping model, only the rounds in which a node is awake are counted for the awake complexity, while sleeping rounds are ignored. This is motivated by the fact that a node spends resources only in its awake rounds and hence the goal is to minimize the awake complexity.Our framework allows us to design distributed MIS algorithms that have ${\mathcal{O}}({\text{polyloglog }}n)$ (worst-case) awake complexity in certain important graph classes which satisfy the so-called adjacency property. Informally, the adjacency property guarantees that the graph can be partitioned into an appropriate number of classes so that each node has at least one neighbor belonging to every class. Graphs that can satisfy the adjacency property are random graphs with large clustering coefficient such as random geometric graphs as well as line graphs of regular (or near regular) graphs.We first apply our framework to design two randomized distributed MIS algorithms for random geometric graphs of arbitrary dimension d (even non-constant). The first algorithm has ${\mathcal{O}}({\text{polyloglog }}n)$ (worst-case) awake complexity with high probability, where n is the number of nodes in the graph.1This means that any node in the network spends only ${\mathcal{O}}({\text{polyloglog }}n)$ awake rounds; this is almost exponentially better than the (traditional) time complexity of ${\mathcal{O}}({\text{log }}n)$ rounds (where there is no distinction between awake and sleeping rounds) known for distributed MIS algorithms on general graphs or even the faster ${\mathcal{O}}\left({\sqrt {\frac{{{\text{log }}n}}{{{\text{loglog }}n}}} }\right)$ rounds known for Erdos-Renyi random graphs. However, the (traditional) time complexity of our first algorithm is quite large—essentially proportional to the degree of the graph. Our second algorithm has a slightly worse awake complexity of ${\mathcal{O}}(d\,{\text{polyloglog }}n)$, but achieves a significantly better time complexity of ${\mathcal{O}}(d\,\log n\,{\text{polyloglog }}n)$ rounds whp.We also show that our framework can be used to design ${\mathcal{O}}({\text{polyloglog }}n)$ awake complexity MIS algorithms in other types of random graphs, namely an augmented Erdos-Renyi random graph that has a large clustering coefficient.

Many exceptionally high-quality doctoral dissertations were submitted for the 2022 Principles of Distributed Computing Doctoral Dissertation Award. After careful long deliberation, the award committee decided to share the award among two:

We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in Õ(D+√n) rounds in the standard CONGEST model (where n is the network size and D is the network diameter) and this is essentially the best possible round complexity (up to logarithmic factors). However, in resource-constrained networks such as wireless ad hoc and sensor networks, nodes spending so much time can lead to significant spending of resources such as energy.

Performing computation in the presence of faulty and malicious nodes is a central problem in distributed computing. Over 35 years ago, Dwork, Peleg, Pippenger, and Upfal [STOC 1986, SICOMP 1988] studied the fundamental Byzantine agreement problem in sparse, bounded degree networks and presented the first protocol that achieved almost-everywhere agreement among good nodes. However, this protocol and several subsequent protocols including that of King, Saia, Sanwalani, and Vee [FOCS 2006] had the drawback that they were not fully-distributed - in those protocols, nodes are required to have initial knowledge of the entire network topology. This drawback makes such protocols not applicable to real-world communication networks such as peer-to-peer (P2P) networks, which are typically sparse and bounded degree and where nodes initially have only local knowledge of themselves and of their neighbors.

A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC 2017, Elkin, PODC 2017]. However, it is open whether a singularly (near) optimal bound can be obtained for the MST construction problem in general \emph{asynchronous} CONGEST networks. We present a randomized distributed MST algorithm that, with high probability, computes an MST in \emph{asynchronous} CONGEST networks and takes $\tilde{O}(D^{1+ε} + \sqrt{n})$ time and $\tilde{O}(m)$ messages, where $n$ is the number of nodes, $m$ the number of edges, $D$ is the diameter of the network, and $ε>0$ is an arbitrarily small constant (both time and message bounds hold with high probability). Our algorithm is message optimal (up to a polylog$(n)$ factor) and almost time optimal (except for a $D^ε$ factor). Our result answers an open question raised in Mashregi and King [DISC 2019] by giving the first known asynchronous MST algorithm that has sublinear time (for all $D = O(n^{1-ε})$) and uses $\tilde{O}(m)$ messages. Using a result of Mashregi and King [DISC 2019], this also yields the first asynchronous MST algorithm that is sublinear in both time and messages in the $KT_1$ CONGEST model. A key tool in our algorithm is the construction of a low diameter rooted spanning tree in asynchronous CONGEST that has depth $\tilde{O}(D^{1+ε})$ (for an arbitrarily small constant $ε> 0$) in $\tilde{O}(D^{1+ε})$ time and $\tilde{O}(m)$ messages. To the best of our knowledge, this is the first such construction that is almost singularly optimal in the asynchronous setting.

We study several fundamental problems in the k-machine model, a message-passing model for large-scale distributed computations where $k\geq 2$ machines jointly perform computations on a large input of size N, (typically, $N\gg k$). The input is initially partitioned (randomly or in a balanced fashion) among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation.Our main result is a general technique for designing efficient deterministic distributed algorithms in the k-machine model using PRAM algorithms. Our technique works by efficiently simulating PRAM algorithms in the k-machine model in a deterministic way. This simulation allows us to arrive at new algorithms in the k-machine model for some problems for which no efficient k-machine algorithms are known before and also improve on existing results in the k-machine model for some problems.While our simulation allows us to obtain k-machine algorithms for any problem with a known PRAM algorithm, we mainly focus on graph problems. For an input graph on n vertices and m edges, we obtain $\tilde{O}(m/k^{2})$ round4algorithms for various graph problems such as r-connectivity for $r=1,2,3,4$, minimum spanning tree (MST), maximal independent set (MIS), $(\Delta+1)$-coloring, maximal matching, ear decomposition, and spanners under the assumption that the edges of the input graph are partitioned (randomly, or in an arbitrary, but balanced, fashion) among the k machines. For problems such as connectivity and MST, the above bound is (essentially) the best possible (up to logarithmic factors). Our simulation technique allows us to obtain the first known efficient deterministic algorithms in the k-machine model for other problems with known deterministic PRAM algorithms.4$\tilde{O}$ notation hides a polylog $(.)$ factor and an additive polylog $(.)$ term.

We will present the fundamentals of Byzantine agreement and leader election problems from a modern perspective. Byzantine fault tolerant protocols are at the heart of secure and robust protocols that can tolerate the presence of malicious nodes in a distributed system, such as a Peer-to-Peer (P2P) network, which allows a large number of peers to enter the network with little or no admission control. Such malicious peers acting alone or in collaboration can cause disruption of service in P2P systems.

We study the communication cost (or message complexity) of fundamental distributed symmetry breaking problems, namely, coloring and MIS. While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems. In fact, all known algorithms need at least Ω(m) communication for these problems, where m is the number of edges in the graph. We addressthe following question in this paper: can we solve problems such as coloring and MIS using sublinear, i.e., o(m) communication, and if sounder what conditions?

This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in asynchronous networks. Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for general synchronous networks that ran in O(D) time and used O(m log n) messages (where D, m, and n are the network’s diameter, number of edges and number of nodes, respectively) with high probability. Both bounds are near optimal (up to a logarithmic factor), since Ω(D) and Ω(m) are the respective lower bounds for time and messages for leader election even for synchronous networks and even for (Monte-Carlo) randomized algorithms. On the other hand, for general asynchronous networks, leader election algorithms are only known that are either time or message optimal, but not both. Kutten et al. (DISC 2020) presented a randomized asynchronous leader election algorithm that is singularly near optimal for complete networks, but left open the problem for general networks. This paper shows that singularly near optimal (up to polylogarithmic factors) bounds can be achieved for general asynchronous networks. We present a randomized singularly near optimal leader election algorithm that runs in O(D + log² n) time and O(m log² n) messages with high probability. Our result is the first known distributed leader election algorithm for asynchronous networks that is near optimal with respect to both time and message complexity and improves over a long line of results including the classical results of Gallager et al. (ACM TOPLAS, 1983), Peleg (JPDC, 1989), and Awerbuch (STOC, 89).

The well-studied influence maximization problem involves choosing a seed set of a given size, which maximizes the expected influence. However, such solutions might have a significant probability of achieving low influence, which might not be suitable in many applications. In this paper, we consider a different approach: find a seed set that maximizes the influence set size with a given probability. We show that this objective is not submodular, and design a greedy, multi-criteria approximation algorithm for this problem with rigorous approximation guarantees. We also evaluate our algorithm on multiple datasets, and show that they have similar or better quality as the ones optimizing the expected influence, but with additional guarantees on the probability.

Triangles are an important pattern in large-scale graph analysis for their practical use in many real-life applications. However, with the expansion of networks, maintaining a balanced computational load is challenging especially for problems like triangle computations because of skewed vertices. On the other hand, there is a huge amount of data in database management systems (DBMSs) that can be modeled and analyzed as graphs. With these motivations in mind, we developed PandaSQL, a novel approach using SQL queries to enumerate all the triangles in a given graph based on Randomized Triangle Enumeration Algorithm. Our approach is elegant, abstract, and short compared to traditional languages like C++ or Python. Moreover, our partitioning queries ensures perfect load balancing. Thus, the triangle enumeration is independent, local, and parallel.

Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the worst-case time for all nodes to finish. The best-known (randomized) MIS algorithms take O(log n) worst-case rounds on general graphs (where n is the number of nodes). Breaking the O(log n) worst-case bound has been a longstanding open problem, while currently the best-known lower bound is [EQUATION] rounds.

With the rise of dynamic reconfigurable networks such as Peer-to-Peer (P2P) networks, overlay networks, ad hoc wireless and mesh networks, it has become important to construct and maintain topologies with various desirable properties (such as connectivity, low diameter, expansion, low degree etc.) in an efficient decentralized manner. The main result of this paper is a distributed protocol called DConstructor that given any (connected) network topology will "converge" to a given (desired) target topology such as an expander, hypercube, or Chord, with high probability. Our protocol is efficient, lightweight, and scalable, and it incurs only O(polylog(n)) overhead (where n is the network size) for topology construction and maintenance: only polylogarithmic (in n) bits need to be processed and sent by each node per round, the convergence time is polylogarithmic rounds and any node's computation cost per round is also polylogarithmic. Our protocol is robust and self-repairing in the sense that it will converge to the desired topology in polylogarithmic rounds and polylogarithmic communication cost under dynamic topology changes and arbitrary insertions and deletions of nodes.

The K-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of n data points with labels and a query point q, we want to assign a label to q based on the labels of the K-nearest points to the query. We study this problem in the k-machine model, a model for distributed large-scale data. In this model, we assume that the n points are distributed (in a balanced fashion) among the k machines and the goal is to compute an answer given a query point to a machine using a small number of communication rounds.

Motivated, in part, by the rise of permissionless systems such as Bitcoin where arbitrary nodes (whose identities are not known apriori) can join and leave at will, we extend established research in scalable Byzantine agreement to a more practical model where each node (initially) does not know the identity of other nodes. A node can send to new destinations only by sending to random (or arbitrary) nodes, or responding (if it chooses) to messages received from those destinations. We assume a synchronous and fully-connected network, with a full-information, but static Byzantine adversary. A general drawback of existing Byzantine protocols is that the communication cost incurred by the honest nodes may not be proportional to those incurred by the Byzantine nodes; in fact, they can be significantly higher. Our goal is to design Byzantine protocols for fundamental problems which are {\em resource competitive}, i.e., the number of bits sent by honest nodes is not much more than those sent by Byzantine nodes. We describe a randomized scalable algorithm to solve Byzantine agreement, leader election, and committee election in this model. Our algorithm sends an expected $O((T+n)\log n)$ bits and has latency $O(polylog(n))$, where $n$ is the number of nodes, and $T$ is the minimum of $n^2$ and the number of bits sent by adversarially controlled nodes. The algorithm is resilient to $(1/4-ε)n$ Byzantine nodes for any fixed $ε> 0$, and succeeds with high probability. Our work can be considered as a first application of resource-competitive analysis to fundamental Byzantine problems. To complement our algorithm we also show lower bounds for resource-competitive Byzantine agreement. We prove that, in general, one cannot hope to design Byzantine protocols that have communication cost that is significantly smaller than the cost of the Byzantine adversary.

This paper presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity.This algorithm runs in Õ(D + √ n) time and exchanges Õ(m) messages (both with high probability), where n is the number of nodes of the network, D is the hop-diameter, and m is the number of edges.This is the first distributed MST algorithm that matches simultaneously the time lower bound of Ω(D + √ n) [Elkin, SIAM J. Comput.2006] and the message lower bound of Ω(m) [Kutten et al., J. ACM 2015], which both apply to randomized Monte Carlo algorithms.The prior time and message lower bounds are derived using two completely different graph constructions; the existing lower bound construction that shows one lower bound does not work for the other.To complement our algorithm, we present a new lower bound graph construction for which any distributed MST algorithm requires both Ω(D + √ n) rounds and Ω(m) messages.

This paper investigates the message complexity of distributed information spreading in adversarial dynamic networks. While distributed computations in dynamic networks have been studied intensively over the last years, almost all of the existing work solely focuses on the time complexity of distributed algorithms. In information spreading, the goal is to spread k tokens of information to every node on an n-node network. We consider the amortized (average) message complexity of spreading a token, assuming that the number of tokens is large. In a static network, this basic problem can be solved using (asymptotically optimal) O(n) amortized messages per token. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. We present two sets of results depending on how nodes send messages to their neighbors: 1. Local broadcast: We show a tight lower bound of Ω̃(n2) on the number of amortized local broadcasts, which is matched by the naive flooding algorithm. The lower bound holds for randomized algorithms against a strongly adaptive adversary. 2. Unicast: We study the message complexity as a function of the number of dynamic changes in the network. To facilitate this, we introduce adversary-competitive message complexity as a natural complexity measure for analyzing dynamic networks: The adversary pays a unit cost for every topological change and the message cost of an algorithm is determined as the actual number of messages sent minus the total cost of the adversary. Under this model, we give a deterministic algorithm that obtains an optimal amortized message complexity of O(n) if the number of tokens k is sufficiently large. We also present a randomized algorithm that achieves subquadratic amortized message complexity for much smaller k under an oblivious adversary.

Designing effective algorithms for community detection is an important and challenging problem in large-scale graphs, studied extensively in the literature. Various solutions have been proposed, but many of them are centralized with expensive procedures (requiring full knowledge of the input graph) and have a large running time. In this paper, we present a distributed algorithm for community detection in the stochastic block model (also called planted partition model), a widely-studied and canonical random graph model for community detection and clustering. Our algorithm called CDRW(Community Detection by Random Walks) is based on random walks, and is localized and lightweight, and easy to implement. A novel feature of the algorithm is that it uses the concept of local mixing time to identify the community around a given node. We present a rigorous theoretical analysis that shows that the algorithm can accurately identify the communities in the stochastic block model and characterize the model parameters where the algorithm works. We also present experimental results that validate our theoretical analysis. We also analyze the performance of our distributed algorithm under the CONGEST distributed model as well as the k-machine model, a model for large-scale distributed computations, and show that it can be efficiently implemented.

We study the fundamental problem of counting the number of nodes in a sparse network (of unknown size) under the presence of a large number of Byzantine nodes. We assume the full information model where the Byzantine nodes have complete knowledge about the entire state of the network at every round (including random choices made by all the nodes), have unbounded computational power, and can deviate arbitrarily from the protocol. Essentially all known algorithms for fundamental Byzantine problems (e.g., agreement, leader election, sampling) studied in the literature assume the knowledge (or at least an estimate) of the size of the network. It is nontrivial to design algorithms for Byzantine problems that work without knowledge of the network size, especially in boundeddegree (expander) networks where the local views of all nodes are (essentially) the same and limited, and Byzantine nodes can quite easily fake the presence/absence of non-existing nodes. To design truly local algorithms that do not rely on any global knowledge (including network size), estimating the size of the network under Byzantine nodes is an important first step. Our main contribution is a randomized distributed algorithm that estimates the size of a network under the presence of a large number of Byzantine nodes. In particular, our algorithm estimates the size of a sparse, “small-world”, expander network with up to O(n1-δ) Byzantine nodes, where n is the (unknown) network size and δ > 0 can be be any arbitrarily small (but fixed) constant. Our algorithm outputs a (fixed) constant factor estimate of log(n) with high probability; the correct estimate of the network size will be known to a large fraction ((1 - ϵ)fraction, for any fixed positive constant ϵ) of the honest nodes. Our algorithm is fully distributed, lightweight, and simple to implement, runs in O(log3n) rounds, and requires nodes to send and receive messages of only small-sized messages per round; any node's local computation cost per round is also small.

We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the G(n, p) random graph model, with number of nodes n and p = c ln n/n^δ (for any constant 00), that finds a Hamiltonian cycle with high probability in Õ(n^δ) rounds. Our algorithm works in the (synchronous) CONGEST model (i.e., only O(log n)-sized messages are communicated per edge per round) and its computational cost per node is sublinear (in n) per round and is fully-distributed (each node uses only o(n) memory and all nodes' computations are essentially balanced). Our algorithm improves over the previous best known result in terms of both the running time as well as the edge sparsity of the graphs where it can succeed; in particular, the denser the random graph, the smaller is the running time.

The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We introduce a new notion of mixing of a random walk on a (undirected) graph, called local mixing. Informally, the local mixing with respect to a given node s, is the mixing of a random walk probability distribution restricted to a large enough subset of nodes - say, a subset of size at least n/β for a given parameter β - containing s. The time to mix over such a subset by a random walk starting from a source node s is called the local mixing time with respect to s. The local mixing time captures the local connectivity and expansion properties around a given source node and is a useful parameter that determines the running time of algorithms for partial information spreading, gossip etc. Our first contribution is formally defining the notion of local mixing time in an undirected graph. We then present an efficient distributed algorithm which computes a constant factor approximation the local mixing time with respect to a source node s in Õ(Ts) rounds1where Tsis the local mixing time w.r.t s in an n-node regular graph. This bound holds when Tsis significantly smaller than the conductance of the local mixing set (i.e., the set where the walk mixes locally); this is typically the interesting case where the local mixing time is significantly smaller than the mixing time (with respect to s). We also present a distributed algorithm that computes the exact local mixing time in Õ(TsD) rounds, where D = min{Ts, D} and D is the diameter of the graph (this bound holds unconditionally without any assumptions on Ts). Our algorithms work in the CONGEST model of distributed computing. Since the local mixing time can be significantly smaller than the mixing time (or even the diameter) in many graphs, it serves as a tighter measure of distributed complexity in certain algorithmic applications. In particular, we show that local mixing time tightly characterizes the complexity of partial information spreading which in turn is useful in solving other problems such as the maximum coverage problem, full information spreading, leader election etc.

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n >> k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main contribution is the General Lower Bound Theorem , a theorem that can be used to show non-trivial lower bounds on the round complexity of distributed large-scale data computations. This result is established via an information-theoretic approach that relates the round complexity to the minimal amount of information required by machines to solve the problem. Our approach is generic, and this theorem can be used in a “cookbook” fashion to show distributed lower bounds for several problems, including non-graph problems. We present two applications by showing (almost) tight lower bounds on the round complexity of two fundamental graph problems, namely, PageRank computation and triangle enumeration . These applications show that our approach can yield lower bounds for problems where the application of communication complexity techniques seems not obvious or gives weak bounds, including and especially under a stochastic partition of the input. We then present distributed algorithms for PageRank and triangle enumeration with a round complexity that (almost) matches the respective lower bounds; these algorithms exhibit a round complexity that scales superlinearly in k , improving significantly over previous results [Klauck et al., SODA 2015]. Specifically, we show the following results: PageRank: We show a lower bound of Ὼ(n/k 2 ) rounds and present a distributed algorithm that computes an approximation of the PageRank of all the nodes of a graph in Õ(n/k 2 ) rounds. Triangle enumeration: We show that there exist graphs with m edges where any distributed algorithm requires Ὼ(m/k 5/3 ) rounds. This result also implies the first non-trivial lower bound of Ὼ(n 1/3 ) rounds for the congested clique model, which is tight up to logarithmic factors. We then present a distributed algorithm that enumerates all the triangles of a graph in Õ(m/k 5/3 + n/k 4/3 ) rounds.

This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems. We consider the synchronous CONGEST distributed computing model and assume that each node has initial knowledge of itself and the identifiers of its neighbors - the so-called KT_1 model - a well-studied model that also naturally arises in many applications. Recently, it has been established that one can obtain (almost) singularly optimal algorithms, i.e., algorithms that have simultaneously optimal time and message complexity (up to polylogarithmic factors), for many fundamental problems in the standard KT_0 model (where nodes have only local knowledge of themselves and not their neighbors). The situation is less clear in the KT_1 model. In this paper, we present several new distributed algorithms in the KT_1 model that trade off between time and message complexity. Our distributed algorithms are based on a uniform and general approach which involves constructing a sparsified spanning subgraph of the original graph - called a danner - that trades off the number of edges with the diameter of the sparsifier. In particular, a key ingredient of our approach is a distributed randomized algorithm that, given a graph G and any delta in [0,1], with high probability constructs a danner that has diameter O~(D + n^{1-delta}) and O~(min{m,n^{1+delta}}) edges in O~(n^{1-delta}) rounds while using O~(min{m,n^{1+delta}}) messages, where n, m, and D are the number of nodes, edges, and the diameter of G, respectively. Using our danner construction, we present a family of distributed randomized algorithms for various fundamental problems that exhibit a trade-off between message and time complexity and that improve over previous results. Specifically, we show the following results (all hold with high probability) in the KT_1 model, which subsume and improve over prior bounds in the KT_1 model (King et al., PODC 2014 and Awerbuch et al., JACM 1990) and the KT_0 model (Kutten et al., JACM 2015, Pandurangan et al., STOC 2017 and Elkin, PODC 2017): 1) Leader Election, Broadcast, and ST. These problems can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,1]. 2) MST and Connectivity. These problems can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5]. In particular, for delta = 0.5 we obtain a distributed MST algorithm that runs in optimal O~(D+sqrt{n}) rounds and uses O~(min{m,n^{3/2}}) messages. We note that this improves over the singularly optimal algorithm in the KT_0 model that uses O~(D+sqrt{n}) rounds and O~(m) messages. 3) Minimum Cut. O(log n)-approximate minimum cut can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5]. 4) Graph Verification Problems such as Bipartiteness, Spanning Subgraph etc. These can be solved in O~(D+n^{1-delta}) rounds using O~(min{m,n^{1+delta}}) messages for any delta in [0,0.5].

We study local symmetry breaking problems in the Congest model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem. Our work is motivated by the following central question: can we break the long-standing Θ(log n) time-complexity barrier and the Θ(m) message-complexity barrier in the Congest model for MIS or closely-related symmetry breaking problems?

This paper presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in Õ(D + √n) time and exchanges Õ(m) messages (both with high probability), where n is the number of nodes of the network, D is the diameter, and m is the number of edges. This is the first distributed MST algorithm that matches simultaneously the time lower bound of Ω(D + √n) [Elkin, SIAM J. Comput. 2006] and the message lower bound of Ω(m) [Kutten et al., J. ACM 2015], which both apply to randomized Monte Carlo algorithms.

We study local symmetry breaking problems in the Congest model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem. The time (round) complexity of MIS (and ruling sets) have attracted much attention in the Local model. Indeed, recent results (Barenboim et al., FOCS 2012, Ghaffari SODA 2016) for the MIS problem have tried to break the long-standing O(log n)-round "barrier" achieved by Luby's algorithm, but these yield o(log n)-round complexity only when the maximum degree Delta is somewhat small relative to n. More importantly, these results apply only in the Local model. In fact, the best known time bound in the Congest model is still O(log n) (via Luby's algorithm) even for moderately small Delta (i.e., for Delta = Omega(log n) and Delta = o(n)). Furthermore, message complexity has been largely ignored in the context of local symmetry breaking. Luby's algorithm takes O(m) messages on m-edge graphs and this is the best known bound with respect to messages. Our work is motivated by the following central question: can we break the Theta(log n) time complexity barrier and the Theta(m) message complexity barrier in the Congest model for MIS or closely-related symmetry breaking problems? This paper presents progress towards this question for the distributed ruling set problem in the Congest model. A beta-ruling set is an independent set such that every node in the graph is at most beta hops from a node in the independent set. We present the following results: - Time Complexity: We show that we can break the O(log n) "barrier" for 2- and 3-ruling sets. We compute 3-ruling sets in O(log n/log log n) rounds with high probability (whp). More generally we show that 2-ruling sets can be computed in O(log Delta (log n)^(1/2 + epsilon) + log n/log log n) rounds for any epsilon > 0, which is o(log n) for a wide range of Delta values (e.g., Delta = 2^(log n)^(1/2-epsilon)). These are the first 2- and 3-ruling set algorithms to improve over the O(log n)-round complexity of Luby's algorithm in the Congest model. - Message Complexity: We show an Omega(n^2) lower bound on the message complexity of computing an MIS (i.e., 1-ruling set) which holds also for randomized algorithms and present a contrast to this by showing a randomized algorithm for 2-ruling sets that, whp, uses only O(n log^2 n) messages and runs in O(Delta log n) rounds. This is the first message-efficient algorithm known for ruling sets, which has message complexity nearly linear in n (which is optimal up to a polylogarithmic factor).

Volunteer computing is being used successfully for large scale scientific computations. This research is in the context of Volpex, a programming framework that supports communicating parallel processes in a volunteer environment. Redundancy and checkpointing are combined to ensure consistent forward progress with Volpex in this unique execution environment characterized by heterogeneous failure prone nodes and interdependent replicated processes. An important parameter for optimizing performance with Volpex is the frequency of checkpointing. The paper presents a mathematical model to minimize the completion time for inter-dependent parallel processes running in a volunteer environment by finding a suitable checkpoint interval. Validation is performed with a sample real world application running on a pool of distributed volunteer nodes. The results indicate that the performance with our predicted checkpoint interval is fairly close to the best performance obtained empirically by varying the checkpoint interval.

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n gg k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in ~O(n/k2) rounds (~O notation hides a polylog(n) factor and an additive polylog(n) term). This improves over the best previously known bound of ~O(n/k) [Klauck et al., SODA 2015], and is optimal (up to a polylogarithmic factor) in view of an existing lower bound of ~Ω(n/k2). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. We then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take ~O(n/k2) rounds, and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of ~Ω(n/k2) for many graph verification problems using lower bounds in random-partition communication complexity.

We present a fully-distributed self-healing algorithm dex that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders—whose expansion properties hold deterministically—that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only probabilistic guarantees on the network expansion which rapidly degrade in a dynamic setting; in particular, the expansion properties can degrade even more rapidly under adversarial insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only $$O(\log n)$$ rounds and $$O(\log n)$$ messages are needed with high probability (n is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table on top of dex with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have guaranteed properties (constant bounded degree and expansion) despite dynamic changes.

Motivated by the need for designing efficient and robust fully-distributed computation in highly dynamic networks such as Peer-to-Peer (P2P) networks, we study distributed protocols for constructing and maintaining dynamic network topologies with good expansion properties. Our goal is to maintain a sparse (bounded degree) expander topology despite heavy churn (i.e., Nodes joining and leaving the network continuously over time). We assume that the churn is controlled by an adversary that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is a randomized distributed protocol that guarantees with high probability the maintenance of a constant degree graph with high expansion even under continuous high adversarial churn. Our protocol can tolerate a churn rate of up to O(n/polylog(n)) per round (where n is the stable network size). Our protocol is efficient, lightweight, and scalable, and it incurs only O(polylog(n)) overhead for topology maintenance: only polylogarithmic(in n) bits needs to be processed and sent by each node per round and any node's computation cost per round is also polylogarithmic. The given protocol is a fundamental ingredient that is needed for the design of efficient fully-distributed algorithms for solving fundamental distributed computing problems such as agreement, leader election, search, and storage in highly dynamic P2P networks and enables fast and scalable algorithms for these problems that can tolerate a large amount of churn.

We study two fundamental graph problems, Graph Connectivity (GC) and Minimum Spanning Tree (MST), in the well-studied Congested Clique model, and present several new bounds on the time and message complexities of randomized algorithms for these problems. No non-trivial (i.e., super-constant) time lower bounds are known for either of the aforementioned problems; in particular, an important open question is whether or not constant-round algorithms exist for these problems. We make progress toward answering this question by presenting randomized Monte Carlo algorithms for both problems that run in O(log log log n) rounds (where n is the size of the clique). Our results improve by an exponential factor on the long-standing (deterministic) time bound of O(log log n) rounds for these problems due to Lotker et al. (SICOMP 2005). Our algorithms make use of several algorithmic tools including graph sketching, random sampling, and fast sorting.

Motivated by the increasing need for fast distributed processing of large-scale graphs such as the Web graph and various social networks, we study a number of fundamental graph problems in the message-passing model, where we have k machines that jointly perform computation on an arbitrary n-node (typically, n ≫ k) input graph. The graph is assumed to be randomly partitioned among the k ≥ 2 machines (a common implementation in many real world systems). The communication is point-to-point, and the goal is to minimize the time complexity, i.e., the number of communication rounds, of solving various fundamental graph problems. We present lower bounds that quantify the fundamental time limitations of distributively solving graph problems. We first show a lower bound of Ω(n/k) rounds for computing a spanning tree (ST) of the input graph. This result also implies the same bound for other fundamental problems such as computing a minimum spanning tree (MST), breadth-first tree (BFS), and shortest paths tree (SPT). We also show an Ω(n/k2) lower bound for connectivity, ST verification and other related problems. Our lower bounds develop and use new bounds in random-partition communication complexity. To complement our lower bounds, we also give algorithms for various fundamental graph problems, e.g., PageRank, MST, connectivity, ST verification, shortest paths, cuts, spanners, covering problems, densest subgraph, subgraph isomorphism, finding triangles, etc. We show that problems such as PageRank, MST, connectivity, and graph covering can be solved in Õ(n/k) time (the notation Õ hides polylog(n) factors and an additive polylog(n) term); this shows that one can achieve almost linear (in k) speedup, whereas for shortest paths, we present algorithms that run in time (for (1 + ε)-factor approximation) and in time (for O(log n)-factor approximation) respectively. Our results step towards understanding the complexity of distributively solving large-scale graph problems.

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This article focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most “obvious” complexity bounds have not been proven for randomized algorithms. In particular, the seemingly obvious lower bounds of Ω( m ) messages, where m is the number of edges in the network, and Ω( D ) time, where D is the network diameter, are nontrivial to show for randomized (Monte Carlo) algorithms. (Recent results, showing that even Ω( n ), where n is the number of nodes in the network, is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms, except for the restricted case of comparison algorithms, where it was also required that nodes may not wake up spontaneously and that D and n were not known. We establish these fundamental lower bounds in this article for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (namely, algorithms that work for all graphs), apply to every D , m , and n , and hold even if D , m , and n are known, all the nodes wake up simultaneously, and the algorithms can make any use of node's identities. To show that these bounds are tight, we present an O ( m ) messages algorithm. An O ( D ) time leader election algorithm is known. A slight adaptation of our lower bound technique gives rise to an Ω( m ) message lower bound for randomized broadcast algorithms. An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. The answer is known to be negative in the deterministic setting. We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that tradeoff messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.

We present a fully-distributed self-healing algorithm DEX, that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders - whose expansion properties hold deterministically - that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only probabilistic guarantees on the network expansion which rapidly degrade in a dynamic setting, in particular, the expansion properties can degrade even more rapidly under adversarial insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only O(log n) rounds and O(log n) messages are needed with high probability (n is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table (DHT) on top of DEX, with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have guaranteed properties (constant bounded degree and expansion) despite dynamic changes.

The focus of this paper is on quantum distributed computation, where we investigate whether quantum communication can help in speeding up distributed network algorithms. Our main result is that for certain fundamental network problems such as minimum spanning tree, minimum cut, and shortest paths, quantum communication does not help in substantially speeding up distributed algorithms for these problems compared to the classical setting.

We study Byzantine agreement in dynamic networks where topology can change from round to round and nodes can also experience heavy churn (i.e., nodes can join and leave the network continuously over time). Our main contributions are randomized distributed algorithms that achieve almost-everywhere Byzantine agreement with high probability even under a large number of adaptively chosen Byzantine nodes and continuous adversarial churn in a number of rounds that is polylogarithmic in n (where n is the stable network size). We show that our algorithms are essentially optimal (up to polylogarithmic factors) with respect to the amount of Byzantine nodes and churn rate that they can tolerate by showing a lower bound. In particular, we present the following results:

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This paper focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most "obvious" complexity bounds have not been proven for randomized algorithms. The "obvious" lower bounds of Ω(m) messages (m is the number of edges in the network) and Ω(D) time (D is the network diameter) are non-trivial to show for randomized (Monte Carlo) algorithms. (Recent results that show that even Ω(n) (n is the number of nodes in the network) is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms (except for the limited case of comparison algorithms, where it was also required that some nodes may not wake up spontaneously, and that D and n were not known).

We study how to spread k tokens of information to every node on an n-node dynamic network, the edges of which are changing at each round. This basic gossip problem can be completed in O(n + k) rounds in any static network, and determining its complexity in dynamic networks is central to understanding the algorithmic limits and capabilities of various dynamic network models. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying and forwarding them. We first consider the strongly adaptive adversary model where in each round, each node first chooses a token to broadcast to all its neighbors (without knowing who they are), and then an adversary chooses an arbitrary connected communication network for that round with the knowledge of the tokens chosen by each node. We show that Ω(nk/log n + n) rounds are needed for any randomized (centralized or distributed) token-forwarding algorithm to disseminate the k tokens, thus resolving an open problem raised in [KLO10]. The bound applies to a wide class of initial token distributions, including those in which each token is held by exactly one node and well-mixed ones in which each node has each token independently with a constant probability. Our result for the strongly adaptive adversary model motivates us to study the weakly adaptive adversary model where in each round, the adversary is required to lay down the network first, and then each node sends a possibly distinct token to each of its neighbors. We propose a simple randomized distributed algorithm where in each round, along every edge (u, v), a token sampled uniformly at random from the symmetric difference of the sets of tokens held by node u and node v is exchanged. We prove that starting from any well-mixed distribution of tokens where each node has each token independently with a constant probability, this algorithm solves the k-gossip problem in O((n + k) log n log k) rounds with high probability over the initial token distribution and the randomness of the protocol. We then show how the above uniform sampling problem can be solved using Õ(log n) bits of communication, making the overall algorithm communication-efficient. We next present a centralized algorithm that solves the gossip problem for every initial distribution in O((n + k) log2 n) rounds in the offline setting where the entire sequence of communication networks is known to the algorithm in advance. Finally, we present an -round centralized offline algorithm in which each node can only broadcast a single token to all of its neighbors in each round.

We study robust and efficient distributed algorithms for searching, storing, and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to guarantee, despite high node churn rate, that a large number of nodes in the network can store, retrieve, and maintain a large number of data items. Our main contributions are fast randomized distributed algorithms that guarantee the above with high probability even under high adversarial churn. In particular, we present the following main results:

We study a distributed randomized information propagation mechanism in networks we call the coalescing-branching random walk (cobra walk, for short). A cobra walk is a generalization of the well-studied "standard" random walk, and is useful in modeling and understanding the Susceptible-Infected Susceptible (SIS)-type of epidemic processes in networks. It can also be helpful in performing light-weight information dissemination in resource-constrained networks. A cobra walk is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. (For instance, this could be a node that has a piece of data, rumor, or a virus.) In each step of a cobra walk, each active node chooses k random neighbors to become active for the next step ("branching"). A node is active for step t + 1 only if it is chosen by an active node in step t ("coalescing"). This results in a stochastic process in the underlying network with properties that are quite different from both the standard random walk (which is equivalent to the cobra walk with branching factor 1) as well as other gossip-based rumor spreading mechanisms.

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this article, we focus on the problem of sampling random walks efficiently in a distributed network and its applications. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain random walk samples. All previous algorithms that compute a random walk sample of length ℓ as a subroutine always do so naively, that is, in O (ℓ) rounds. The main contribution of this article is a fast distributed algorithm for performing random walks. We present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. Our algorithm performs a random walk of length ℓ in Õ (√ℓ D ) rounds ( Õ hides polylog n factors where n is the number of nodes in the network) with high probability on an undirected network, where D is the diameter of the network. For small diameter graphs, this is a significant improvement over the naive O (ℓ) bound. Furthermore, our algorithm is optimal within a poly-logarithmic factor as there exists a matching lower bound [Nanongkai et al. 2011]. We further extend our algorithms to efficiently perform k independent random walks in Õ (√ k ℓ D + k ) rounds. We also show that our algorithm can be applied to speedup the more general Metropolis-Hastings sampling. Our random-walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine. We present two main applications. First, we give a fast distributed algorithm for computing a random spanning tree (RST) in an arbitrary (undirected unweighted) network which runs in Õ (√ mD ) rounds with high probability ( m is the number of edges). Our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks.

Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer membership management. While several such algorithms are ubiquitous, and use numerous random walk samples, the walks themselves have always been performed naively. In this paper, we focus on the problem of performing random walk sampling efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds and messages required to obtain several random walk samples in a continuous online fashion. We present the first round and message optimal distributed algorithms that present a significant improvement on all previous approaches. The theoretical analysis and comprehensive experimental evaluation of our algorithms show that they perform very well in different types of networks of differing topologies. In particular, our results show how several random walks can be performed continuously (when source nodes are provided only at runtime, i.e., online), such that each walk of length ℓ can be performed exactly in just Õ(√ℓD) rounds (where D is the diameter of the network), and O(ℓ) messages. This significantly improves upon both, the naive technique that requires O(ℓ) rounds and O(ℓ) messages, and the sophisticated algorithm of [13] that has the same round complexity as this paper but requires Ω(m√ℓ) messages (where m is the number of edges in the network). Our theoretical results are corroborated through extensive experiments on various topological data sets. Our algorithms are fully decentralized, lightweight, and easily implementable, and can serve as building blocks in the design of topologically-aware networks.

Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience heavy node churn (i.e., nodes join and leave the network continuously over time). Our goal is to design fast algorithms (running in a small number of rounds) that guarantee, despite high node churn rate, that almost all nodes reach a stable agreement. Our main contributions are randomized distributed algorithms that guarantee stable almost-everywhere agreement with high probability even under high adversarial churn in a polylogarithmic number of rounds. In particular, we present the following results: 1. An O(log n)-round (n is the stable network size) randomized algorithm that achieves almost-everywhere agreement with high probability under up to linear churn per round (i.e., εn, for some small constant ε > 0), assuming that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). 2. An O(log m log3 n)-round randomized algorithm that achieves almost-everywhere agreement with high probability under up to ε√n churn per round (for some small ε > 0), where m is the size of the input value domain, that works even under an adaptive adversary (that also knows the past random choices made by the algorithm). Our algorithms are the first-known, fully-distributed, agreement algorithms that work under highly dynamic settings (i.e., high churn rates per step). Furthermore, they are localized (i.e., do not require any global topological knowledge), simple, and easy to implement. These algorithms can serve as building blocks for implementing other non-trivial distributed computing tasks in dynamic P2P networks.

We study randomized gossip-based processes in dynamic networks that are motivated by information discovery in large-scale distributed networks such as peer-to-peer and social networks. A well-studied problem in peer-to-peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self-stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network --- new edges are added to the network --- and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications.

Distance computation (e.g., computing shortest paths) is one of the most fundamental primitives used in communication networks. The cost of effectively and accurately computing pairwise network distances can become prohibitive in large-scale networks such as the Internet and Peer-to-Peer (P2P) networks. To negotiate the rising need for very efficient distance computation at scales never imagined before, approximation techniques for numerous variants of this question have recently received significant attention in the literature. Several different areas of theoretical research have emerged centered around this problem, such as metric embeddings, distance labelings, spanners, and distance oracles. The goal is to preprocess the graph and store a small amount of information such that whenever a query for any pairwise distance is issued, the distance can be well approximated (i.e., with small stretch) very quickly in an online fashion. Specifically, the pre-processing (usually) involves storing a small sketch with each node, such that at query time only the sketches of the concerned nodes need to be looked up to compute the approximate distance. Techniques derived from metric embeddings have been considered extensively by the networking community, usually under the name of network coordinate systems. On the other hand, while the computation of distance oracles has received considerable attention in the context of web graphs and social networks, there has been little work towards similar algorithms within the networking community. In this paper, we present the first theoretical study of distance sketches derived from distance oracles in a distributed network. We first present a fast distributed algorithm for computing approximate distance sketches, based on a distributed implementation of the distance oracle scheme of [Thorup-Zwick, JACM 2005]. We also show how to modify this basic construction to achieve different tradeoffs between the number of pairs for which the distance estimate is accurate, the size of the sketches, and the time and message complexity necessary to compute them. These tradeoffs can then be combined to give an efficient construction of small sketches with provable average-case as well as worst-case performance. Our algorithms use only small-sized messages and hence are suitable for bandwidth-constrained networks, and can be used in various networking applications such as topology discovery and construction, token management, load balancing, monitoring overlays, and several other problems in distributed algorithms.

Motivated by applications to modern networking technologies, there has been interest in designing efficient gossip-based protocols for computing aggregate functions. While gossip-based protocols provide robustness due to their randomized nature, reducing the message and time complexity of these protocols is also of paramount importance in the context of resource-constrained networks such as sensor and peer-to-peer networks. We present provably time-optimal efficient gossip-based algorithms for aggregate computation with almost optimal message complexity. Given an n-node network, our algorithms guarantee that all the nodes can compute the common aggregates (such as Max, Min, Average, Sum, and Count) of their values in optimal $O(\log n)$ time and using $O(n \log \log n)$ messages. Our result improves on the algorithm of Kempe, Dobra, and Gehrke [Proceedings of the IEEE Annual Symposium on Foundations of Computer Science, 2003, pp. 482–491] that is time-optimal but uses $O(n \log n)$ messages, as well as on the algorithm of Kashyap et al. [Proceedings of Symposium on Principles of Database Systems, 2006, pp. 308–317] that uses $O(n \log \log n)$ messages but is not time-optimal (takes $O(\log n \log \log n)$ time). Furthermore, we show that our algorithms can be used to improve gossip-based aggregate computation in sparse communication networks, such as in peer-to-peer networks. The main technical ingredient of our algorithm is a technique called distributed random ranking (DRR) that can be useful in other applications as well. DRR gives an efficient distributed procedure to partition the network into a forest of (disjoint) trees of small size. Since the size of each tree is small, aggregates within each tree can be efficiently obtained at their respective roots. All the roots then perform a uniform gossip algorithm on their local aggregates to reach a distributed consensus on the global aggregates. Our algorithms are non-address-oblivious. In contrast, we show a lower bound of $\Omega(n\log n)$ on the message complexity of any address-oblivious algorithm for computing aggregates. This shows that non-address-oblivious algorithms are needed to obtain significantly better message complexity. Our lower bound holds regardless of the number of rounds taken or the size of the messages used. Our lower bound is the first nontrivial lower bound for gossip-based aggregate computation and also gives the first formal proof that computing aggregates is strictly harder than rumor spreading in the address-oblivious model.

We study the verification problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some properties, e.g., if it is a tree or if it is connected (every node knows at the end of the process whether $H$ has the specified property or not). We would like to perform this verification in a decentralized fashion via a distributed algorithm. The time complexity of verification is measured as the number of rounds of distributed communication. In this paper we initiate a systematic study of distributed verification and give almost tight lower bounds on the running time of distributed verification algorithms for many fundamental problems such as connectivity, spanning connected subgraph, and $s$-$t$ cut verification. We then show applications of these results in deriving strong unconditional time lower bounds on the hardness of distributed approximation for many classical optimization problems including minimum spanning tree (MST), shortest paths, and minimum cut. Many of these results are the first nontrivial lower bounds for both exact and approximate distributed computation, and they resolve previous open questions. Moreover, our unconditional lower bound of approximating MST subsumes and improves upon the previous hardness of approximation bound of Elkin [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456] as well as the lower bound for (exact) MST computation of Peleg and Rubinovich [D. Peleg and V. Rubinovich, SIAM J. Comput., 30 (2000), pp. 1427--1442]. Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm for any approximation factor. Our lower bound proofs show an interesting connection between communication complexity and distributed computing which turns out to be useful in establishing the time complexity of exact and approximate distributed computation of many problems.

We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show that a random walk of length l on a network of diameter D can be performed in Õ(√{l D}+D) time. A major question left open is whether there exists a faster algorithm, especially whether the multiplication of √{l} and √{D} is necessary.

We consider the problem of self-healing in reconfigurable networks (e.g. peer-to-peer and wireless mesh networks) that are under repeated attack by an omniscient adversary and propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, also keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We use a model similar to that used in recent work on self-healing. In our model, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds by quick repairs, which consist of adding or deleting edges in an efficient localized manner.These repairs preserve the edge expansion, spectral gap, and network stretch, after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, the expansion of the graph will be either 'better' than the expansion of the graph formed by considering only the adversarial insertions (not the adversarial deletions) or the expansion will be, at least, a constant. Also, the stretch i.e. the distance between any pair of nodes in the healed graph is no more than a O(log n) factor. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most O(κ d) in the actual graph, for a small parameter κ. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Our distributed data structure has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] and Forgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.

We study the verification problem in distributed networks, stated as follows. Let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H. We would like to verify whether H has some properties, e.g., if it is a tree or if it is connected (every node knows in the end of the process whether H has the specified property or not). We would like to perform this verification in a decentralized fashion via a distributed algorithm. The time complexity of verification is measured as the number of rounds of distributed communication.

We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. Our algorithm performs a random walk of length l in Õ(√l D) rounds (with high probability) on an undirected network, where D is the diameter of the network. This improves over the previous best algorithm that ran in Õ(l2/3D1/3) rounds (Das Sarma et al., PODC 2009). We further extend our algorithms to efficiently perform k independent random walks in Õ(√kl D + k) rounds. We then show that there is a fundamental difficulty in improving the dependence on l any further by proving a lower bound of Ω(√l/log l + D) under a general model of distributed random walk algorithms. Our random walk algorithms are useful in speeding up distributed algorithms for a variety of applications that use random walks as a subroutine. We present two main applications. First, we give a fast distributed algorithm for computing a random spanning tree (RST) in an arbitrary (undirected) network which runs in Õ(√mD) rounds (with high probability; here m is the number of edges). Our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks.

Motivated by applications to modern networking technologies, there has been interest in designing efficient gossip-based protocols for computing aggregate functions. While gossip-based protocols provide robustness due to their randomized nature, reducing the message and time complexity of these protocols is also of paramount importance in the context of resource-constrained networks such as sensor and peer-to-peer networks. We present the first provably almost-optimal gossip-based algorithms for aggregate computation that are both time optimal and message-optimal. Given a n-node network, our algorithms guarantee that all the nodes can compute the common aggregates (such as Min, Max, Count, Sum, Average, Rank etc.) of their values in optimal O(log n) time and using O(n log log n) messages. Our result improves on the algorithm of Kempe et al. [9] that is time-optimal, but uses O(n log n) messages as well as on the algorithm of Kashyap et al. [8] that uses O(n log log n) messages, but is not time-optimal (takes O(log n log log n) time). Furthermore, we show that our algorithms can be used to improve gossip-based aggregate computation in sparse communication networks, such as in peer-to-peer networks. The main technical ingredient of our algorithm is a technique called distributed random ranking

Topology control in ad hoc networks is a multi-criteria optimization problem involving (contradictory) objectives of connectivity, interference, and power minimization. Additionally, nodes can be unreliable, which adds another dimension to an already challenging problem. In this paper, we study topology control problems in ad hoc networks under node failures for arbitrary node distributions. We consider a simple and natural stochastic failure model, in which each node can fail independently with a given probability. The topology control problem under stochastic failures is to choose a power level for each node and a subset of edges such that the residual graph (i.e., the graph formed by the nodes which have not failed) is connected and can be scheduled efficiently, with high probability. We develop provably efficient bi-criteria approximation algorithms for this problem that simultaneously minimize power, reduce interference, and ensure that the surviving graph is connected with high probability. Our algorithms can be implemented efficiently in a distributed manner.

We present DRR-gossip, an energy-efficient and robust aggregate computation algorithm in sensor networks. We prove that the DRR-gossip algorithm requires O(n) messages and O(n3/2/log1/2 n) one-hop wireless transmissions to obtain aggregates on a random geometric graph. This reduces the energy consumption by at least a factor of 1/log n over the standard uniform gossip algorithm. Experiments validate the theoretical results and show that DRR-gossip needs much less transmissions than other gossip-based schemes.

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample.

Traditionally, the performance of distributed algorithms has been measured in terms of time and message complexity.Message complexity concerns the number of messages transmitted over all the edges during the course of the algorithm. However, in energy-constrained ad hoc wireless networks (e.g., sensor networks), energy is a critical factor in measuring the efficiency of a distributed algorithm. Transmitting a message between two nodes has an associated cost (energy) and moreover this cost can depend on the two nodes (e.g., the distance between them among other things). Thus in addition to the time and message complexity, it is important to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm. This paper addresses the minimum spanning tree (MST) problem, a fundamental problem in distributed computing and communication networks. We study energy-efficient distributed algorithms for the Euclidean MST problem assuming random distribution of nodes. We show a non-trivial lower bound ofΩ(log n)on the energy complexity of any distributed MST algorithm. We then give an energy-optimal distributed algorithm that constructs an optimal MST with energy complexityO(log n)on average andO(log n log log n)with high probability. This is an improvement over the previous best known bound on the average energy complexity ofΩ(log2). Our energy-optimal algorithm exploits a novel property of the giant component of sparse random geometric graphs. All of the above results assume that nodes do not know their geometric coordinates. If the nodes know their own coordinates, then we give an algorithm withO(1)energy complexity (which is the best possible) that gives anO(1)approximation to the MST.

While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time; this makes these algorithms impractical for resource-constrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energy-efficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate the theoretical results and show that the bounds are much better in practice.

MOTIVATION: Complementing its traditional role in structural studies of proteins, nuclear magnetic resonance (NMR) spectroscopy is playing an increasingly important role in functional studies. NMR dynamics experiments characterize motions involved in target recognition, ligand binding, etc., while NMR chemical shift perturbation experiments identify and localize protein-protein and protein-ligand interactions. The key bottleneck in these studies is to determine the backbone resonance assignment, which allows spectral peaks to be mapped to specific atoms. This article develops a novel approach to address that bottleneck, exploiting an available X-ray structure or homology model to assign the entire backbone from a set of relatively fast and cheap NMR experiments. RESULTS: We formulate contact replacement for resonance assignment as the problem of computing correspondences between a contact graph representing the structure and an NMR graph representing the data; the NMR graph is a significantly corrupted, ambiguous version of the contact graph. We first show that by combining connectivity and amino acid type information, and exploiting the random structure of the noise, one can provably determine unique correspondences in polynomial time with high probability, even in the presence of significant noise (a constant number of noisy edges per vertex). We then detail an efficient randomized algorithm and show that, over a variety of experimental and synthetic datasets, it is robust to typical levels of structural variation (1-2 AA), noise (250-600%) and missings (10-40%). Our algorithm achieves very good overall assignment accuracy, above 80% in alpha-helices, 70% in beta-sheets and 60% in loop regions. AVAILABILITY: Our contact replacement algorithm is implemented in platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

We present a uniform approach to design efficient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar (FRT embedding). We show how to efficiently compute an (implicit) FRT embedding in a decentralized manner and how to use the embedding to obtain expected O(log n)-approximate distributed algorithms for the generalized Steiner forest problem, the minimum routing cost spanning tree problem, and the $k$-source shortest paths problem in arbitrary networks. The time complexities of our algorithms are within a polylogarithmic factor of the optimum.

Traditionally, the performance of distributed algorithms has been measured in terms of time and message complexity. Message complexity concerns the number of messages transmitted over all the edges during the course of the algorithm. However, in energy-constraint radio or wireless networks (e.g., sensor networks), energy is a critical factor in measuring the efficiency of a distributed algorithm. Transmitting a message between two nodes has an associated cost (energy) and moreover this cost can depend on the two nodes (e.g., the distance between them among other things). Thus in addition to the time and message complexity, it is important to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm, and design energy-efficient distributed algorithms for energy-constraint networks.

We focus in this work on an aspect of online computation that is not addressed by standard competitive analysis, namely, identifying request sequences for which nontrivial online algorithms are useful versus request sequences for which all algorithms perform equally poorly. The motivations for this work are advanced system and architecture designs which allow the operating system to dynamically allocate resources to online protocols such as prefetching and caching. To utilize these features, the operating system needs to identify data streams that can benefit from more resources.

This paper focuses on the principled study of distance reconstruction for distance-based node localization. We address an important issue in node localization by showing that a highly incomplete set of inter-node distance measurements obtained in ad-hoc node deployments carries sufficient information for the accurate reconstruction of the missing distances, even in the presence of noise and sensor node failures. We provide an efficient and provably accurate algorithm for this reconstruction, and we show that the resulting error is bounded, decreasing at a rate that is inversely proportional to radicn, the square root of the number of nodes in the region of deployment. Although this result is applicable to many localization schemes, in this paper we illustrate its use in conjunction with the popular multidimensional scaling algorithm. Our analysis reveals valuable insights and key factors to consider during the sensor network setup phase, to improve the quality of the position estimates

MOTIVATION: Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call 'contact-based', seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (nuclear Overhauser enhancement spectroscopy, NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were 'close enough'. Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g. for alpha-helices and beta-sheets) within a graph and by mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise. RESULTS: This paper develops, analyzes and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500% noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet datasets. Our approach is able to eliminate a large majority of noise edges and to uncover large consistent sets of interactions. AVAILABILITY: Our algorithm has been implemented in the platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

A wireless sensor network consists of a large number of small, resource-constrained devices and usually operates in hostile environments that are prone to link and node failures. Computing aggregates such as average, minimum, maximum and sum is fundamental to various primitive functions of a sensor network, such as system monitoring, data querying, and collaborative information processing. In this paper, we present and analyze a suite of randomized distributed algorithms to efficiently and robustly compute aggregates. Our distributed random grouping (DRG) algorithm is simple and natural and uses probabilistic grouping to progressively converge to the aggregate value. DRG is local and randomized and is naturally robust against dynamic topology changes from link/node failures. Although our algorithm is natural and simple, it is nontrivial to show that it converges to the correct aggregate value and to bound the time needed for convergence. Our analysis uses the eigenstructure of the underlying graph in a novel way to show convergence and to bound the running time of our algorithms. We also present simulation results of our algorithm and compare its performance to various other known distributed algorithms. Simulations show that DRG needs far fewer transmissions than other distributed localized schemes

A wireless sensor network consists of a large number of small, resource-constrained devices and usually operates in hostile environments that are prone to link and node failures. Computing aggregates such as average, minimum, maximum and sum is fundamental to various primitive functions of a sensor network like system monitoring, data querying, and collaborative information processing. In this paper we present and analyze a suite of randomized distributed algorithms to efficiently and robustly compute aggregates. Our distributed random grouping (DRG) algorithm is simple and natural and uses probabilistic grouping to progressively converge to the aggregate value. DRG is local and randomized and is naturally robust against dynamic topology changes from link/node failures. Although our algorithm is natural and simple, it is nontrivial to show that it converges to the correct aggregate value and to bound the time needed for convergence. Our analysis uses the eigen-structure of the underlying graph in a novel way to show convergence and to bound the running time of our algorithms. We also present simulation results of our algorithm and compare its performance to various other known distributed algorithms. Simulations show that DRG needs much less transmissions than other distributed localized schemes, namely gossip and broadcast flooding.

We present a universal algorithm for the classical online problem of caching or demand paging. We consider the caching problem when the page request sequence is drawn from an unknown probability distribution and the goal is to devise an efficient algorithm whose performance is close to the optimal online algorithm which has full knowledge of the underlying distribution. Most previous works have devised such algorithms for specific classes of distributions with the assumption that the algorithm has full knowledge of the source. In this paper, we present a universal and simple algorithm based on pattern matching for mixing sources (includes Markov sources). The expected performance of our algorithm is within 4 + o(1) times the optimal online algorithm (which has full knowledge of the input model and can use unbounded resources)

No abstract available.

Nuclear magnetic resonance (NMR) spectroscopy allows scientists to study protein structure, dynamics, and interactions in solution. A necessary first step for such applications is determining the resonance assignment, mapping spectral data to atoms and residues in the primary sequence. Automated resonance assignment algorithms rely on information regarding connectivity (e.g. through-bond atomic interactions) and amino acid type, typically using the former to determine strings of connected residues and the latter to map those strings to positions in the primary sequence. Significant ambiguity exists in both connectivity and amino acid type, and different algorithms have combined the information in two phases (find short unambiguous strings then align) or simultaneously (align while extending strings). This paper focuses on the information content available in connectivity alone, allowing for ambiguity rather than handling only unambiguous strings, and complements existing work on the information content in amino acid type.In this paper, we develop a novel random-graph theoretic framework for algorithmic analysis of NMR sequential assignment. Our random graph model captures the structure of chemical shift degeneracy (a key source of connectivity ambiguity). We then give a simple and natural randomized algorithm for finding an optimum sequential cover. The algorithm naturally and efficiently reuses substrings while exploring connectivity choices; it overcomes local ambiguity by enforcing global consistency of all choices. We employ our random graph model to analyze our algorithm, and show that it can provably tolerate a relatively large ambiguity while still giving expected optimal performance in polynomial time. To study the algorithm's performance in practice, we tested it on experimental data sets from a variety of proteins and experimental set-ups. The algorithm was able to overcome significant noise and local ambiguity and consistently identify significant sequential fragments.

Peer-to-peer (P2P) computing has emerged as a significant paradigm for providing distributed services, in particular search and data sharing. Current P2P networks (e.g., Gnutella) are constructed by participants following their own uncoordinated (and often whimsical) protocols; they consequently suffer from frequent network overload and partitioning into disconnected pieces separated by choke points with inadequate bandwidth. We propose a protocol for participants to build P2P networks in a distributed fashion, and prove that it results in connected networks of constant degree and logarithmic diameter. These properties are crucial for efficient search and data exchange. An important feature of our protocol is that it operates without global knowledge of all the nodes in the network.

In a peer-to-peer (P2P) network, nodes connect into an existing network and participate in providing and availing of services. There is no dichotomy between a central server and distributed clients. Current P2P networks (e.g., Gnutella) are constructed by participants following their own uncoordinated (and often whimsical) protocols; they consequently suffer from frequent network overload and fragmentation into disconnected pieces separated by choke-points with inadequate bandwidth. The authors propose a simple scheme for participants to build P2P networks in a distributed fashion, and prove that it results in connected networks of constant degree and logarithmic diameter. It does so with no global knowledge of all the nodes in the network. In the most common P2P application to date (search), these properties are important.

Article Free Access Share on Static and dynamic evaluation of QoS properties Authors: Gopal Pandurangan Computer Science Department, Brown University, Box 1910, Providence, RI Computer Science Department, Brown University, Box 1910, Providence, RIView Profile , Eli Upfal Computer Science Department, Brown University, Box 1910, Providence, RI Computer Science Department, Brown University, Box 1910, Providence, RIView Profile Authors Info & Claims STOC '99: Proceedings of the thirty-first annual ACM symposium on Theory of ComputingMay 1999 Pages 566–573https://doi.org/10.1145/301250.301404Published:01 May 1999Publication History 0citation237DownloadsMetricsTotal Citations0Total Downloads237Last 12 Months10Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF