A Multinomial Logit (MNL) model is composed of a finite universe of items [n] = {1,…,n}, each assigned a positive weight. A query specifies an admissible subset - called a slate - and the model chooses one item from that slate with probability proportional to its weight. This query model is also known as the Plackett-Luce model or conditional sampling oracle in the literature. Although MNLs have been studied extensively, a basic computational question remains open: given query access to slates, how efficiently can we learn weights so that, for every slate, the induced choice distribution is within total variation distance ε of the ground truth? This question is central to MNL learning and has direct implications for modern recommender system interfaces. We provide two algorithms for this task, one with adaptive queries and one with non‑adaptive queries. Each algorithm outputs an MNL M̂ that induces, for each slate S, a distribution M̂_S on S that is within ε total variation distance of the true distribution. Our adaptive algorithm makes O(n/ε³ log n) queries, while our non-adaptive algorithm makes O(n²/ε³ log n log(n/ε)) queries. Both algorithms query only slates of size two and run in time proportional to their query complexity. We complement these upper bounds with lower bounds of Ω(n/ε² log n) for adaptive queries and Ω(n²/ε² log n) for non‑adaptive queries, thus proving that our adaptive algorithm is optimal in its dependence on the support size n, while the non-adaptive one is tight within a log n factor.

Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio. In this paper we show that no algorithm can achieve a competitive ratio better than 1−e^{1-e}=0.82062..., improving upon the 0.823 upper bound presented in Manshadi, Oveis Gharan and Saberi (2011). Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1−e^{-1}, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.

A Random Utility Model (RUM) is a classical model of user behavior defined by a distribution over $\mathbb{R}^n$. A user, presented with a subset of $\\{1,\ldots,n\\}$, will select the item of the subset with the highest utility, according to a utility vector drawn from the specified distribution. In practical settings, the subset is often of small size, as in the ``ten blue links'' of web search. In this paper, we consider a learning setting with complete information on user choices from subsets of size at most $k$. We show that $k=\Theta(\sqrt{n})$ is both necessary and sufficient to predict the distribution of all user choices with an arbitrarily small, constant error. Based on the upper bound, we obtain new algorithms for approximate RUM learning and variations thereof. Furthermore, we employ our lower bound for approximate RUM learning to derive lower bounds to fractional extensions of the well-studied $k$-deck and trace reconstruction problems.

Abstract Forecasting players in sports has grown in popularity due to the potential for a tactical advantage and the applicability of such research to multi-agent interaction systems. Team sports contain a significant social component that influences interactions between teammates and opponents. However, it still needs to be fully exploited. In this work, we hypothesize that each participant has a specific function in each action and that role-based interaction is critical for predicting players’ future moves. We create RolFor, a novel end-to-end model for Role-based Forecasting. RolFor uses a new module we developed called Ordering Neural Networks (OrderNN) to permute the order of the players such that each player is assigned to a latent role. The latent role is then modeled with a RoleGCN. Thanks to its graph representation, it provides a fully learnable adjacency matrix that captures the relationships between roles and is subsequently used to forecast the players’ future trajectories. Extensive experiments on a challenging NBA basketball dataset back up the importance of roles and justify our goal of modeling them using optimizable models. When an oracle provides roles, the proposed RolFor compares favorably to the current state-of-the-art (it ranks first in terms of ADE and second in terms of FDE errors). However, training the end-to-end RolFor incurs the issues of differentiability of permutation methods, which we experimentally review. Finally, this work restates differentiable ranking as a difficult open problem and its great potential in conjunction with graph-based interaction models.

In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best approximates the given distribution on average. Our algorithm is based on a linear program that we solve using the ellipsoid method. Given that its separation oracle problem is NP-hard, we devise an approximate separation oracle that can be viewed as a generalization of the weighted Feedback Arc Set problem to hypergraphs. Our theoretical result can also be made practical: we obtain a heuristic that scales to real-world datasets.

Othello, also known as Reversi, is a popular 2-players board game. Olivaw is an intelligent agent playing Othello. Compared to the most famous ones (such as Saio), it exploits limited resources by autonomously learning how to improve its gameplay by playing against itself. In previous occasions, Othello players reported the impression of a sort of human-likeness in how Olivaw plays. We designed and ran an experimental study to better investigate these impressions in a controlled setting. Participants were asked to watch the moves of pre-recorded Othello games played by a human expert player against either another agent (i.e., Olivaw, Saio) or another human. The identity of the opponent, the outcome of the game (i.e., whether the human expert or the opponent player won), and the color of the players (i.e., black or white, black always playing first) were manipulated. We then asked participants to evaluate the human-likeness of the opponent player. Results confirm that the outcome of the match affects the perception of human-likeness of the players.

In this article, we introduceOlivaw, an artificial intelligenceOthelloplayer adopting the design principles of the famous AlphaGo programs. The main motivation behindOlivawis to attain exceptional competence in a nontrivial board game at a tiny fraction of the cost of its illustrious predecessors. In this article, we show how the AlphaGo Zero’s paradigm can be successfully applied to the popular game ofOthellousing only commodity hardware and free cloud services. While being simpler thanChessorGo,Othellomaintains a considerable search space and difficulty in evaluating board positions. To achieve this result,Olivawimplements some improvements inspired by recent works to accelerate the standard AlphaGo Zero learning process. The main modification implies doubling the positions collected per game during the training phase, by including also positions not played but largely explored by the agent. We tested the strength ofOlivawin three different ways: by pitting it against Edax, considered by the strongest open-sourceOthelloengine, by playing anonymous games on the web platform OthelloQuest, and, finally, in two in-person matches against top-notch human players: a national champion and a former world champion.

Correlation Clustering is an important clustering problem with many applications. We study the reconstruction version of this problem, in which one seeks to reconstruct a latent clustering that has been corrupted by random noise and adversarial modifications. Concerning the latter, there is a standard "post-adversarial" model in the literature, in which adversarial modifications come after the noise. Here, we introduce and analyse a "pre-adversarial" model, in which adversarial modifications come before the noise. Given an input coming from such a semi-adversarial generative model, the goal is to approximately reconstruct with high probability the latent clustering. We focus on the case where the hidden clusters have nearly equal size and show the following. In the pre-adversarial setting, spectral algorithms are optimal, in the sense that they reconstruct all the way to the information-theoretic threshold beyond which no reconstruction is possible. This is in contrast to the post-adversarial setting, in which their ability to restore the hidden clusters stops before the threshold, but the gap is optimally filled by SDP-based algorithms. These results highlight a heretofore unknown robustness of spectral algorithms, showing them less brittle than previously thought.

Random utility models (RUMs) encode the likelihood that a particular item will be selected from a slate of competing items. RUMs are well-studied objects in both discrete choice theory and, more recently, in the machine learning community, as they encode a fairly broad notion of rational user behavior. In this paper, we focus on slates of size two representing head-to-head contests. Given a tournament matrix $M$ such that $M_{i,j}$ is the probability that item $j$ will be selected from $\{i, j\}$, we consider the problem of finding the RUM that most closely reproduces $M$. For this problem we obtain a polynomial-time algorithm returning a RUM that approximately minimizes the average error over the pairs. Our experiments show that RUMs can perfectly represent many of the tournament matrices that have been considered in the literature; in fact, the maximum average error induced by RUMs on the matrices we considered is negligible ($\approx 0.001$). We also show that RUMs are competitive, on prediction tasks, with previous approaches.

Olivaw is an AI Othello playing agent which autonomously learns how to improve its gameplay by playing against itself. Some top-notch players (including former World Champions) reported that they had the impression that Olivaw's gameplay was human-like. To better investigate the processes related to these impressions, we conducted a pilot study using the Othello Game Evaluation App, a computer application we developed to evaluate pre-recorded Othello games in a controlled setting while assuring an adequate user experience. An exploratory analysis of the results shows that the participants mostly evaluated Olivaw as a human. When asked for a motivation for their choice, some of them reported that they evaluate poor game moves (and, consequently, losing the game) as an indication of the human-likeness of the player.

The Edsger W. Dijkstra Prize in Distributed Computing is awarded for outstanding papers on the principles of distributed computing, whose significance and impact on the theory or practice of distributed computing have been evident for at least a decade. It is sponsored jointly by the ACM Symposium on Principles of Distributed Computing (PODC) and the EATCS Symposium on Distributed Computing (DISC). The prize is presented annually, with the presentation taking place alternately at PODC and DISC.

Clustering problems and clustering algorithms are often overly sensitive to the presence of outliers: even a handful of points can greatly affect the structure of the optimal solution and its cost. This is why many algorithms for robust clustering problems have been formulated in recent years. These algorithms discard some points as outliers, excluding them from the clustering. However, outlier selection can be unfair: some categories of input points may be disproportionately affected by the outlier removal algorithm.

Clustering is a central topic in unsupervised learning and its online formulation has received a lot of attention in recent years. In this paper, we study the classic facility location problem in the presence of multiple machine-learned advice. We design an algorithm with provable performance guarantees such that, if the advice is good, it outperforms the best-known online algorithms for the problem, and if it is bad it still matches their performance.We complement our theoretical analysis with an in-depth study of the performance of our algorithm, showing its effectiveness on synthetic and real-world data sets.

No abstract available.

Understanding information dynamics and their resulting cascades is a central topic in social network analysis. In a recent seminal work, Cheng et al. analyzed multiples cascades on Facebook over several months, and noticed that many of them exhibit a recurring behaviour. They tend to have multiple peaks of popularity, with periods of quiescence in between.

We address the problem of computing the distribution of induced connected subgraphs, aka graphlets or motifs , in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling by leveraging the color coding technique by Alon, Yuster, and Zwick. In this work, we extend the applicability of this approach by introducing a set of algorithmic optimizations and techniques that reduce the running time and space usage of color coding and improve the accuracy of the counts. To this end, we first show how to optimize color coding to efficiently build a compact table of a representative subsample of all graphlets in the input graph. For 8-node motifs, we can build such a table in one hour for a graph with 65M nodes and 1.8B edges, which is times larger than the state of the art. We then introduce a novel adaptive sampling scheme that breaks the “additive error barrier” of uniform sampling, guaranteeing multiplicative approximations instead of just additive ones. This allows us to count not only the most frequent motifs, but also extremely rare ones. For instance, on one graph we accurately count nearly 10.000 distinct 8-node motifs whose relative frequency is so small that uniform sampling would literally take centuries to find them. Our results show that color coding is still the most promising approach to scalable motif counting.

The randomized technique of color coding is behind state-of-the-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we develop novel tools for the "motif counting via color coding" framework. As a result, our new algorithm, MOTIYO, scales to much larger graphs while at the same time providing more accurate motif counts than ever before. This is achieved thanks to two types of improvements. First, we design new succinct data structures for fast color coding operations, and a biased coloring trick that trades accuracy versus resource usage. These optimizations drastically reduce the resource requirements of color coding. Second, we develop an adaptive motif sampling strategy, based on a fractional set cover problem, that breaks the additive approximation barrier of standard sampling. This gives multiplicative approximations for all motifs at once, allowing us to count not only the most frequent motifs but also extremely rare ones. To give an idea of the improvements, in 40 minutes MOTIVO counts 7-nodes motifs on a graph with 65M nodes and 1.8B edges; this is 30 and 500 times larger than the state of the art, respectively in terms of nodes and edges. On the accuracy side, in one hour MOTIVO produces accurate counts of ≈ 10.000 distinct 8-node motifs on graphs where state-of-the-art algorithms fail even to find the second most frequent motif. Our method requires just a high-end desktop machine. These results show how color coding can bring motif mining to the realm of truly massive graphs using only ordinary hardware.

Given a notion of pairwise similarity between objects, locality sensitive hashing (LSH) aims to construct a hash function family over the universe of objects such that the probability two objects hash to the same value is their similarity. LSH is a powerful algorithmic tool for large scale applications and much work has been done to understand LSHable similarities, i.e., similarities that admit an LSH. In this paper we focus on similarities that are provably non-LSHable and propose a notion of distortion to capture the approximation of such a similarity by an LSHable similarity. We consider several well-known non-LSHable similarities and show tight upper and lower bounds on their distortion.

We present a novel approach for LDA (Latent Dirichlet Allocation) topic reconstruction. The main technical idea is to show that the distribution over the documents generated by LDA can be transformed into a distribution for a much simpler generative model in which documents are generated from {\em the same set of topics} but have a much simpler structure: documents are single topic and topics are chosen uniformly at random. Furthermore, this reduction is approximation preserving, in the sense that approximate distributions-- the only ones we can hope to compute in practice-- are mapped into approximate distribution in the simplified world. This opens up the possibility of efficiently reconstructing LDA topics in a roundabout way. Compute an approximate document distribution from the given corpus, transform it into an approximate distribution for the single-topic world, and run a reconstruction algorithm in the uniform, single topic world-- a much simpler task than direct LDA reconstruction. Indeed, we show the viability of the approach by giving very simple algorithms for a generalization of two notable cases that have been studied in the literature, $p$-separability and Gibbs sampling for matrix-like topics.

In this article, we study the completion time of the PUSH-PULL variant of rumor spreading, also known as randomized broadcast. We show that if a network has n nodes and conductance ϕ then, with high probability, PUSH-PULL will deliver the message to all nodes in the graph within O (log n /ϕ) many communication rounds. This bound is best possible. We also give an alternative proof that the completion time of PUSH-PULL is bounded by a polynomial in log n /ϕ, based on graph sparsification. Although the resulting asymptotic bound is not optimal, this proof shows an interesting and, at the outset, unexpected connection between rumor spreading and graph sparsification. Finally, we show that if the degrees of the two endpoints of each edge in the network differ by at most a constant factor, then both PUSH and PULL alone attain the optimal completion time of O (log n /ϕ), with high probability.

Recently, due to the widespread diffusion of smart-phones, mobile puzzle games have experienced a huge increase in their popularity. A successful puzzle has to be both captivating and challenging, and it has been suggested that these features are somehow related to their computational complexity [6]. Indeed, many puzzle games – such as Mah-Jongg, Sokoban, Candy Crush, and 2048, to name a few – are known to be NP-hard [3], [4], [8], [12]. In this paper we consider Trainyard: a popular mobile puzzle game whose goal is to get colored trains from their initial stations to suitable destination stations. We prove that the problem of determining whether there exists a solution to a given Trainyard level is NP-hard. We also provide an implementation of our hardness reduction.

Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets.

Given a pairwise similarity notion between objects, locality sensitive hashing (LSH) aims to construct a hash function family over the universe of objects such that the probability two objects hash to the same value is their similarity. LSH is a powerful algorithmic tool for large-scale applications and much work has been done to understand LSHable similarities, i.e., similarities that admit an LSH. In this paper we focus on similarities that are provably non-LSHable and propose a notion of distortion to capture the approximation of such a similarity by a similarity that is LSHable. We consider several well-known non-LSHable similarities and show tight upper and lower bounds on their distortion. We also experimentally show that our upper bounds translate to e

Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural approaches based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that this approach is outperformed by a carefully engineered version of color coding (CC) [1], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC. Furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC's memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that a careful implementation of CC can push the limits of the state of the art, both in terms of the size of the input graph and of that of the graphlets.

In this paper we introduce a mathematical model that captures some of the salient features of recommender systems that are based on popularity and that try to exploit social ties among the users. We show that, under very general conditions, the market always converges to a steady state, for which we are able to give an explicit form. Thanks to this we can tell rather precisely how much a market is altered by a recommendation system, and determine the power of users to influence others. Our theoretical results are complemented by experiments with real world social networks showing that social graphs prevent large market distortions in spite of the presence of highly influential users.

When individuals in a social network make decisions that depend on what others have done earlier, there is the potential for a cascade to form---a run of behaviors that are highly correlated. In an arbitrary network, the outcome of such a cascade can depend sensitively on the order in which nodes make their decisions, but to date there has been very little investigation of how this dependence works or how to choose an order to optimize various parameters of the cascade. Here we formulate the problem of ordering the nodes in a cascade to maximize the expected number of “favorable” decisions---those that support a given option. We provide an algorithm that ensures an expected linear number of favorable decisions in any graph, and we show that the performance bounds for our algorithm are essentially the best achievable assuming P $\neq$ NP.

The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of prediction tasks in machine learning that require deducing a latent structure from observed patterns of activity in a network, which often require an unrealistically large number of resources (e.g., amount of available data, or computational time). A fundamental question is to understand which properties we can predict with a reasonable degree of accuracy with the available resources, and which we cannot. We define the trace complexity as the number of distinct traces required to achieve high fidelity in reconstructing the topology of the unobserved network or, more generally, some of its properties. We give algorithms that are competitive with, while being simpler and more efficient than, existing network inference approaches. Moreover, we prove that our algorithms are nearly optimal, by proving an information-theoretic lower bound on the number of traces that an optimal inference algorithm requires for performing this task in the general case. Given these strong lower bounds, we turn our attention to special cases, such as trees and bounded-degree graphs, and to property recovery tasks, such as reconstructing the degree distribution without inferring the network. We show that these problems require a much smaller (and more realistic) number of traces, making them potentially solvable in practice.

Sybil attacks in which an adversary forges a potentially unbounded number of identities are a danger to distributed systems and online social networks. The goal of sybil defense is to accurately identify sybil identities. This paper surveys the evolution of sybil defense protocols that leverage the structural properties of the social graph underlying a distributed system to identify sybil identities. We make two main contributions. First, we clarify the deep connection between sybil defense and the theory of random walks. This leads us to identify a community detection algorithm that, for the first time, offers provable guarantees in the context of sybil defense. Second, we advocate a new goal for sybil defense that addresses the more limited, but practically useful, goal of securely white-listing a local region of the graph.

Graphs resulting from human behavior (the web graph, friendship graphs, etc.) have hitherto been viewed as a monolithic class of graphs with similar characteristics; for instance, their degree distributions are markedly heavy tailed. In this paper we take our understanding of behavioral graphs a step further by showing that an intriguing empirical property of web graphs---their compressibility---cannot be exhibited by well-known graph models for the web and for social networks. We then develop a more nuanced model for web graphs and show that it does exhibit compressibility, in addition to previously modeled web graph properties.

When individuals in a social network make decisions that depend on what others have done earlier, there is the potential for a cascade to form --- a run of behaviors that are highly correlated. In an arbitrary network, the outcome of such a cascade can depend sensitively on the order in which nodes make their decisions, but to do date there has been very little investigation of how this dependence works, or how to choose an order to optimize various parameters of the cascade.

We show that some topologies arising naturally in the context of wireless networking are low-degree, expander graphs.

We demonstrate how a recent model of social networks ("Affiliation Networks", [21]) offers powerful cues in local routing within social networks, a theme made famous by sociologist Milgram's "six degrees of separation" experiments. This model posits the existence of an "interest space" that underlies a social network; we prove that in networks produced by this model, not only do short paths exist among all pairs of nodes but natural local routing algorithms can discover them effectively. Specifically, we show that local routing can discover paths of length O(log2 n) to targets chosen uniformly at random, and paths of length O(1) to targets chosen with probability proportional to their degrees. Experiments on the co-authorship graph derived from DBLP data confirm our theoretical results, and shed light into the power of one step of lookahead in routing algorithms for social networks.

We show that if a connected graph with n nodes has conductance ϕ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log4 n/ϕ6) many steps, with high probability, using the PUSH-PULL strategy. An interesting feature of our approach is that it draws a connection between rumour spreading and the spectral sparsification procedure of Spielman and Teng [23].

We show that if a connected graph with $n$ nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within ~O(φ-1 • log n), many rounds with high probability, regardless of the source, by using the PUSH-PULL strategy. The ~O(••) notation hides a polylog φ-1 factor. This result is almost tight since there exists graph of n nodes, and conductance φ, with diameter Ω(φ-1 • log n). If, in addition, the network satisfies some kind of uniformity condition on the degrees, our analysis implies that both both PUSH and PULL, by themselves, successfully broadcast the message to every node in the same number of rounds.

Graphs resulting from human behavior (the web graph, friendship graphs, etc.) have hitherto been viewed as a monolithic class of graphs with similar characteristics; for instance, their degree distributions are markedly heavy-tailed. In this paper we take our understanding of behavioral graphs a step further by showing that an intriguing empirical property of web graphs-their compressibility-cannot be exhibited by well-known graph models for the web and for social networks. We then develop amore nuanced model for web graphs and show that it does exhibit compressibility, in addition to previously modeled web graph properties.

Motivated by structural properties of the Web graph that support efficient data structures for in memory adjacency queries, we study the extent to which a large network can be compressed. Boldi and Vigna (WWW 2004), showed that Web graphs can be compressed down to three bits of storage per edge; we study the compressibility of social networks where again adjacency queries are a fundamental primitive. To this end, we propose simple combinatorial formulations that encapsulate efficient compressibility of graphs. We show that some of the problems are NP-hard yet admit effective heuristics, some of which can exploit properties of social networks such as link reciprocity. Our extensive experiments show that social networks and the Web graph exhibit vastly different compressibility characteristics.

We show that massive attacks against sensor networks that use random key pre-distribution schemes cannot be cheap, provided that the parameters are set in the right way. By choosing them appropriately, any adversary whose aim is to compromise a large fraction of the communication links is forced, with overwhelming probability, to capture a large fraction of the nodes. This holds regardless of the information available to the adversary to select the nodes. We consider two important security properties: We say that the network is unassailable if the adversary cannot compromise a linear fraction of the communication links by compromising a sub-linear fraction of the nodes, and that the network is unsplittable if the adversary cannot partition the network into two (or more) linear size fragments. We show how to set the relevant parameters of random key pre-distribution---pool and key ring size---in such a way that the network is not only connected, but also provably unassailable and unsplittable with high probability. Moreover, we also show how to set the parameters in such a way to form a giant component in the network, a connected subgraph including, say, 99% of the sensors. Giant components emerge by using much smaller key rings, are sparse, and, quite remarkably, are provably unassailable and unsplittable as well. All these results are supported by experiments.

In this paper we give an efficient distributed algorithm computing approximate solutions to a very general, and classical, scheduling problem. The approximation guarantee is within a constant factor of the optimum. By "efficient", we mean that the number of communication rounds is poly-logarithmic in the size of the input. In the problem, we have a bipartite graph with computing agents on one side and resources on the other. Agents that share a resource can communicate in one time step. Each agent has a list of jobs, each with its own length and profit, to be executed on a neighbouring resource within a given time-window. Resources can execute non preemptively only one job at a time. The goal is to maximize the profit of the jobs that are scheduled. It is well known that this problem is NP-hard. A very interesting feature of our algorithm is that it is derived in a systematic manner from a primal-dual algorithm.

We study the problem of optimal skip placement in an inverted list. Assuming the query distribution to be known in advance, we formally prove that an optimal skip placement can be computed quite efficiently. Our best algorithm runs in time O (n log n), n being the length of the list.

In this paper we consider the capacitated vertex cover problem, which is the variant of vertex cover where each node is allowed to cover a limited number of edges. We present an efficient, deterministic, distributed approximation algorithm for the problem. Our algorithm computes a $(2+\epsilon)$-approximate solution which violates the capacity constraints by a factor of $(4+\epsilon)$ in a polylogarithmic number of communication rounds. On the other hand, we also show that every efficient distributed approximation algorithm for this problem must violate the capacity constraints. Our result is achieved in two steps. We first develop a 2-approximate, sequential primal-dual algorithm that violates the capacity constraints by a factor of 2. Subsequently, we present a distributed version of this algorithm. We demonstrate that the sequential algorithm has an inherent need for synchronization which forces any naive distributed implementation to use a linear number of communication rounds. The challenge in this step is therefore to achieve a reduction of the communication complexity to a polylogarithmic number of rounds without worsening the approximation guarantee.

In this article, we consider the problem of computing a minimum-weight vertex-cover in an n -node, weighted, undirected graph G = ( V , E ). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O (log n + log Ŵ ) communication rounds, where Ŵ is the average vertex-weight. The previous best algorithm for this problem requires O (log n (log n + log Ŵ )) rounds and it is not fully distributed. For a maximal matching M in G , it is a well-known fact that any vertex-cover in G needs to have at least | M | vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting.

We give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random predistribution of keys. We also show how to set the parameters---pool and key ring size---in such a way that the network is not only connected with high probability via secure links but also provably resilient, in the following sense: We formally show that any adversary that captures sensors at random with the aim of compromising a constant fraction of the secure links must capture at least a constant fraction of the nodes of the network. In the context of wireless sensor networks where random predistribution of keys is employed, we are the first to provide a mathematically precise proof, with a clear indication of parameter choice, that two crucial properties---connectivity via secure links and resilience against malicious attacks---can be obtained simultaneously. We also show in a mathematically rigorous way that the network enjoys another strong security property. The adversary cannot partition the network into two linear size components, compromising all the links between them, unless it captures linearly many nodes. This implies that the network is also fault tolerant with respect to node failures. Our theoretical results are complemented by extensive simulations that reinforce our main conclusions.

Finding near(est) neighbors is a classic, difficult problem in data management and retrieval, with applications in text and image search,in finding similar objects and matching patterns. Here we study cluster pruning, an extremely simple randomized technique. During preprocessing we randomly choose a subset of data points to be leaders the remaining data points are partitioned by which leader is the closest. For query processing, we find the leader(s) closest to the query point. We then seek the nearest neighbors for the query point among only the points in the clusters of the closest leader(s). Recursion may be used in both preprocessing and in search. Such schemes seek approximate nearest neighbors that are "almost as good" as the nearest neighbors. How good are these approximations and how much do they save in computation.

Search engines rely on Web crawlers to create an index of the Web. Web crawlers explore the Web downloading pages and finding links to new pages to be explored. At any given moment, there are a number of pages waiting to be downloaded in the crawler queue. We study the growth of this queue of pending pages during a crawl of a large subset of the Web. In a normal breadth-first crawler, the queue quickly grows very large. We present a strategy for managing the pending queue that reduces its maximum size by 50% while preserving the coverage and quality of the pages visited. This can be applied to general purpose Web crawlers as well as topic-specific crawling, peer-to-peer search, on-demand Web crawling, and other environments in which memory usage has to be kept to a minimum.

This paper concerns the comparative performance evaluation of protocols for clustering and backbone formation in ad hoc networks characterized by a large number of resource-constrained nodes. Our aim is twofold: we provide the first simulation-based detailed investigation of techniques for clustering and backbone formation that are among the most representative of this area of ad hoc research. Second, we delve into the nature of the selected protocols to assess the effects of the "degree of localization" on their operations, i.e., how being able to execute the protocol based only on local information affects the overall protocol performance. Extensive ns2-based simulation results show that highly localized protocols are rewarded with good performance with respect to all metrics of interest which include protocol duration, energy consumption, message overhead, route length, and backbone size.

In this paper we consider the weighted, capacitated vertex cover problem with hard capacities (capVC). Here, we are given an undirected graph G = (V, E), non-negative vertex weightswtv for all vertices v ∈ V, and node-capacities Bv ≥ 1 for all v ∈ V. A feasible solution to a givencapVC instance consists of a vertex cover C ⊆ V. Each edge e ∈ E is assigned to one of its endpoints in C and the number of edges assigned to any vertex v ∈ C is at most Bv. The goal is to minimize the total weight of C. For a parameter ɛ> 0 we give a deterministic, distributed algorithm for thecapVC problem that computes a vertex cover C of weight at most (2+ɛ)·opt whereopt is the weight of a minimumweight feasible solution to the given instance. The number of edges assigned to any node v ∈ C is at most (4 + ɛ) · Bv. The running time of our algorithm is O(log(nW)/ɛ), where n is the number of nodes in the network and W = wtmax/wtmin is the ratio of largest to smallest weight. This result is complemented by a lower-bound saying that any distributed algorithm forcapVC which requires a poly-logarithmic number of rounds is bound to violate the capacity constraints by a factor two. The main feature of the algorithm is that it is derived in a systematic fashion starting from a primal-dual sequential algorithm.

We propose very simple randomized algorithms to compute sparse overlay networks for geometric random graphs modelling wireless communication networks. The algorithms generate in constant time a sparse overlay network that, with high probability, is connected and spans the whole network. Moreover, by making use of the "power of choice" paradigm, the maximum degree can be made as small as O(log log n), where n is the size of the network. We show the usefulness of this kind of overlays by giving a new protocol for the classical broadcast problem, where a source is to send a message to the whole network. Our experimental evaluation shows that our approach outperforms the well-known gossiping approach in all situations where the cost of a message can be charged to the pair (sender, receiver), i.e. to the edge connecting the two. This includes sensor networks.

Summary form only given. We introduce a novel and unified approach to the problems of device discovery and scatternet formation in multihop Bluetooth networks. By means of ns2 extensive simulations we show that our solution is simple to implement, fast, requires low overhead, both for the device discovery and the scatternet formation phases, and leads to better performance over the major approaches so far proposed in the literature.

We show that some topologies arising naturally in the context of wireless networking are low-degree, expander graphs.

Abstract We address the problem of finding the largest collection of edge‐disjoint cuts in an undirected graph, dubbed CUT PACKING, focusing on its complexity, about which very little is known. We show a very close relationship with INDEPENDENT SET, namely, for the same graph G , the size of the largest cut packing of G is at least the independence number of G , and at most twice that number. This implies that any approximation guarantee for INDEPENDENT SET immediately extends to CUT PACKING within a factor of 2. In particular, this yields a 2‐approximation algorithm for CUT PACKING in perfect graphs. We then present polynomial‐time algorithms for several classes of perfect (and related) graphs, including triangulated graphs and their complements, bipartite graphs and their complements, and Seymour graphs. Finally, we discuss various linear programming relaxations for the problem, finding combinatorial dual problems of CUT PACKING and characterizing the cases in which duality is strong. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 1–11 2004

We show that maximal matchings can be computed deterministically in O(log 4 n ) rounds in the synchronous, message-passing model of computation. This is one of the very few cases known of a nontrivial graph structure, and the only "classical" one, which can be computed distributively in polylogarithmic time without recourse to randomization.

We conduct an experimental analysis of a distributed, randomized algorithm for edge coloring simple undirected graphs. The algorithm is extremely simple, yet, according to the probabilistic analysis, it computes nearly optimal colorings very quickly [12]. We test the algorithm on a number of random as well as non-random graph families.

Certain types of routing, scheduling, and resource-allocation problems in a distributed setting can be modeled as edge-coloring problems. We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation. Our algorithms compute an edge coloring of a graph G with n nodes and maximum degree $\Delta$ with at most $1.6 \Delta + O(\log^{1+ \delta} n)$ colors with high probability (arbitrarily close to 1) for any fixed $\delta > 0$; they run in polylogarithmic time. The upper bound on the number of colors improves upon the $(2 \Delta - 1)$-coloring achievable by a simple reduction to vertex coloring. To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables. The Chernoff--Hoeffding bounds are fundamental tools that are used very frequently in estimating tail probabilities. However, they assume stochastic independence among certain random variables, which may not always hold. Our results extend the Chernoff--Hoeffding bounds to certain types of random variables which are not stochastically independent. We believe that these results are of independent interest and merit further study.

We investigate the relationship between logical expressibility of NP optimization problems and their approximation properties. First such attempt was made by Papadimitrou and Yannakakis (1988), who defined the class of NPO problems MAX NP. We show that many important optimization problems do not belong to MAX NP and that, in fact, there are problems in P which are not in MAX NP. The problems that we consider fit naturally in a new complexity class that we call MAX Π1. We prove that several natural optimization problems are complete for MAX Π1 under approximation-preserving reductions. All these complete problems are not approximable unless P = NP. This motivates the definition of subclasses of MAX Π1 that only contain problems which are presumably eaiser with respect to approximation. In particular, the class that we call RMAX(2) contains approximable problems and problems like MAX CLIQUE that are not known to be nonapproximable. We prove the MAX CLIQUE and several other optimization problems are complete for RMAX(2). All the complete problems in RMAX(2) share the interesting property that they either are nonapproximable or are approximable to any degree of accuracy.

Certain types of routing, scheduling and resource allocation problems in a distributed setting can be modeled as edge coloring problems.We present fast and simple randomized algorithms for edge coloring a graph, in the synchronous distributed point-to-point model of comput ation.Our algorithms compute an edge-coloring of a graph G with n nodes and maximum degree A with at most (1.6 + E)A + logz+d n colors with high probability (arbitrarily close to 1), for any fixed c, 6>0.To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables.Chernoff-Hoeflding bounds are fundamental tools that are used very frequently in estimating tail probabilities.However, they assume stochastic independence among certain random variables, which may not always hold.Our results extend the Chernoff-Hoeffding bounds to certain types of random variables which are not stochastic ally independent.We believe that these results are of independent interest, and merit further study.

This paper deals with the problems of computing a maximal independent set and a vertex coloring in a dktributed model of computation.Given a connected graph G = (V, E) with IVI = n and maximum degree A such that G is neither a complete graph nor an odd cycle, Brooks' theorem shows that G can be colored with A colors.We generalize thk as follows: let G -w be A-colored; then, v can be colored by considering the vertices in an O(loga n) radius around v, and this is tight.Using this, we show that A-coloring G is reducible in 0(log3 n/log A) time to (A+ I)-vertex coloring G in a distributed model.This leads to fast distributed algorithms, and a linear-processor NC algorithm, for Acoloring.We also prove a tight Q(diameter(G)) lower bound for A-edge-coloring bipartite graphs, even with unlimited randomness.When A = 2, this implies an Q(n) lower bound for vertex coloring paths and even cycles.A fundamental notion in distributed graph algorithms is that of a cluster decomposition, introduced by Awerbuch, Goldberg, Luby and Plotkin.We improve the existing bounds by showing how to compute a cluster decomposition in O(n"('(")) ) time, where e(n) = 1/=.This implies improved bounds for several problems, such as computing a maximal independent set and a (A + I )-coloring.We also show how to compute a A-coloring within the same time bound, using our reduction technique.Next, we show that the problem of doing better than O(n"('(m))) time for cluster decomposition is self-reducible to graphs of "intermediate" diameter and degree.This pinpoints the weak points of existing cluster decomposition algorithms.

We investigate tile relationship between logical expressibility of NP optimization problems and their approximation properties.First sucll attempt was made by Papadimitriou and Yannakakis, who defined the class of NPO problems MAX NP.We show that many importaut optimization problems do not belong to MAX NP and that in fact there are problems in P which are not ill lk'IAX NP.The problems that we consider fit naturally in a new complexity class that we call MAX Ill.We prove that several natural optimization problems are complete for MAX H1 under approxima.tionpreserving reductions.All these complete problems are non approximable unless P ¢ NP.This motivates the definition of subclasses of MAX II1 that only contain problems which are presumably easier with respect to approximation.In particular, the class that we call RMAX(2), contains approximable problems and prob-]elllS like MAX CLIQUE that are not known to be nonapproximable.We prove that MAX CLIQUE and several other optimization problems are complete for RMAX(2).

Abstract We consider the problem of predicting whether a deadlock will necessarily occur in a store‐and‐forward network. We define two versions of this problem, depending on whether or not the routes to be followed by packets are fixed. For networks with only one buffer per vertex, both versions of this problem are shown to be NP‐complete even for simple classes of graphs (among others bipartite graphs, two terminal series‐parallel [TTSP] graphs and therefore planar graphs). On the other hand, the same problems are shown to be polynomially solvable for treelike networks. In this case, two efficient algorithms for checking whether a treelike network with n vertices and p packets is bound to deadlock are proposed. The former has an O(pn) time and space complexity, whereas the latter runs in O(n log n)1 time and requires O(n) space. In the case of multibuffered networks, both versions of the problem are shown to be NP‐complete even on treelike networks.