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.

A breakthrough pair of papers by Goel, Kapralov, and Khanna [9, 8] gave the first sublinear-time algorithms for finding large matchings in regular bipartite graphs. In particular, they gave an algorithm based on the idea of randomized depth-first search, that, for any d-regular bipartite graph, finds a perfect matching in O (n log n ) time. (When d = ω(log n ), this is sublinear in the size of the graph.)

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.

Detecting the elements of deception in a conversation is one of the most challenging problems for the AI community. It becomes even more difficult to design a transparent system, which is fully explainable and satisfies the need for financial and legal services to be deployed. This paper presents an approach for fraud detection in transcribed telephone conversations using linguistic features. The proposed approach exploits the syntactic and semantic information of the transcription to extract both the linguistic markers and the sentiment of the customer's response. We demonstrate the results on real-world financial services data using simple, robust and explainable classifiers such as Naive Bayes, Decision Tree, Nearest Neighbours, and Support Vector Machines.

The well-known clustering algorithm of Miller, Peng, and Xu (SPAA 2013) is useful for many applications, including low-diameter decomposition and low-energy distributed algorithms. One nice property of their clustering, shown in previous work by Chang, Dani, Hayes, and Pettie (PODC 2020), is that distances in the cluster graph are rescaled versions of distances in the original graph, up to an O(log n) distortion factor and rounding issues. Minimizing this distortion factor is important for efficiency in computing the clustering, as well as in other applications.

Embedding graphs in a geographical or latent space, i.e. inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We consider the classic model of random geometric graphs where n points are scattered uniformly in a square of area n, and two points have an edge between them if and only if their Euclidean distance is less than r. The reconstruction problem then consists of inferring the vertex positions, up to the symmetries of the square, given only the adjacency matrix of the resulting graph. We give an algorithm that, if r = n^α for α > 0, with high probability reconstructs the vertex positions with a maximum error of O(n^β) where β = 1/2-(4/3)α, until α ≥ 3/8 where β = 0 and the error becomes O(√{log n}). This improves over earlier results, which were unable to reconstruct with error less than r. Our method estimates Euclidean distances using a hybrid of graph distances and short-range estimates based on the number of common neighbors. We extend our results to the surface of the sphere in ℝ³ and to hypercubes in any constant dimension.

Recent work has shown that it is sometimes feasible to significantly reduce the energy usage of some radio-network algorithms by adaptively powering down the radio receiver when it is not needed. Although past work has focused on modifying specific network algorithms in this way, we now ask the question of whether this problem can be solved in a generic way, treating the algorithm as a kind of black box. We are able to answer this question in the affirmative, presenting a new general way to modify arbitrary radio-network algorithms in an attempt to save energy. At the expense of a small increase in the time complexity, we can provably reduce the energy usage to an extent that is provably nearly optimal within a certain class of general-purpose algorithms. As an application, we show that our algorithm reduces the energy cost of breadth-first search in radio networks from the previous best bound of $2^{O(\sqrt{\log n})}$ to $\mathrm{polylog}(n)$, where $n$ is the number of nodes in the network A key ingredient in our algorithm is hierarchical clustering based on additive Voronoi decomposition done at multiple scales. Similar clustering algorithms have been used in other recent work on energy-aware computation in radio networks, but we believe the specific approach presented here may be of independent interest.

We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is O(log2 n), and the time complexity is O(Δ log(n)). Here n is any upper bound on the number of nodes, and Δ is any upper bound on the maximum degree; n and Δ are parameters of our algorithm that we assume are known a priori to all the processors. We note that there exist families of graphs for which our bounds on energy cost and time complexity are simultaneously optimal up to polylog factors, so any significant improvement would need additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of eventual node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present an efficient decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog(n) factor bigger that the optimum.

The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method for sampling and inference. With the advent of Big Data, distributed and parallel variants of MCMC methods are attracting increased attention. In this paper, we give a distributed algorithm that can faithfully simulates sequential single-site Metropolis chains without introducing any bias. When a natural Lipschitz condition for the the Metropolis filters is satisfied, the algorithm can faithfully simulate N-step Metropolis chains within O(N/n + log n) rounds of asynchronous communications, where n is the number of variables. For sequential single-site dynamics, whose mixing requires Ω(n log n) steps, this achieves an optimal linear speedup. For several well-studied graphical models, including proper graph coloring, hardcore model, and Ising model, our condition for linear speedup is much weaker than the uniqueness conditions for the respective models. The novel idea in our algorithm is to resolve updates in advance: the local Metropolis filters can be executed correctly before the full information about neighboring spins is available. This achieves optimal parallelism without introducing any bias.

We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is $O(\log^2 n)$, where $n$ is the size of the network. The total latency of our algorithm is $O(n \log n)$ time steps. We observe that there exist families of network topologies for which both of these bounds are simultaneously optimal up to polylog factors, so any significant improvement will require additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present a decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog($n$) factor bigger that the optimum.

We consider a model of energy complexity in Radio Networks in which transmitting or listening on the channel costs one unit of energy and computation is free. This simplified model captures key aspects of battery-powered sensors: that battery-life is most influenced by transceiver usage, and that at low transmission powers, the actual cost of transmitting and listening are very similar.

Strong spatial mixing (SSM) is a form of correlation decay that has played an essential role in the design of approximate counting algorithms for spin systems. A notable example is the algorithm of Weitz (2006) for the hard-core model on weighted independent sets. We study SSM for the q-colorings problem on the infinite (d+1)-regular tree. Weak spatial mixing (WSM) captures whether the influence of the leaves on the root vanishes as the height of the tree grows. Jonasson (2002) established WSM when q>d+1. In contrast, in SSM, we first fix a coloring on a subset of internal vertices, and we again ask if the influence of the leaves on the root is vanishing. It was known that SSM holds on the (d+1)-regular tree when q>alpha d where alpha ~~ 1.763... is a constant that has arisen in a variety of results concerning random colorings. Here we improve on this bound by showing SSM for q>1.59d. Our proof establishes an L^2 contraction for the BP operator. For the contraction we bound the norm of the BP Jacobian by exploiting combinatorial properties of the coloring of the tree.

A group of n players wants to run a distributed protocol ℘ over a network where communication occurs via private point-to-point channels. Can we efficiently simulate ℘ in the presence of an adversary who knows ℘ and is able to maliciously flip bits on the channels? We show that this is possible, even when L, the number of bits sent in ℘, the average message size α in ℘, and T, the number of bits flipped by the adversary are not known in advance. In particular, we show how to create a robust version of ℘, ℘ such that 1) ℘' fails with probability at most δ, for any δ>0; and 2) ℘' sends O( L (1 + (1/α) łog (n L/δ)) + T) bits. We note that if α is Ω (log (n L/δ), then ℘ sends only O(L+T) bits, and is therefore within a constant factor of optimal. Critically, our result requires that ℘ runs correctly in an asynchronous network and our protocol ℘ must run in a synchronous network.

We study the hard-core (gas) model defined on independent sets of an input graph where the independent sets are weighted by a parameter (aka fugacity) $\lambda>0$. For constant $\Delta$, the previous work of Weitz [ Proceedings of STOC, 2006, pp. 140--149] established an FPTAS for the partition function for graphs of maximum degree $\Delta$ when $\lambda<\lambda_c(\Delta)$. Sly [ Proceedings of FOCS, 2010, pp. 287--296] showed that there is no FPRAS, unless NP=RP, when $\lambda>\lambda_c(\Delta)$. The threshold $\lambda_c(\Delta)$ is the critical point for the statistical physics phase transition for uniqueness/nonuniqueness on the infinite $\Delta$-regular tree. The running time of Weitz's algorithm is exponential in $\log{\Delta}$. Here we present an FPRAS for the partition function whose running time is $O^*(n^2)$. We analyze the simple single-site Markov chain known as the Glauber dynamics for sampling from the associated Gibbs distribution. We prove there exists a constant $\Delta_0$ such that for all graphs with maximum degree $\Delta\geq\Delta_0$ and girth $\geq 7$ (i.e., no cycles of length $\leq 6$), the mixing time of the Glauber dynamics is $O(n\log{n})$ when $\lambda<\lambda_c(\Delta)$. Our work complements that of Weitz, which applies for small constant $\Delta$, whereas our work applies for all $\Delta$ at least a sufficiently large constant $\Delta_0$. (This includes $\Delta$ depending on $n=|V|$.) Our proof utilizes loopy belief propagation (BP) which is a widely used algorithm for inference in graphical models. A novel aspect of our work is using the principal eigenvector for the BP operator to design a distance function which contracts in expectation for pairs of states that behave like the BP fixed point. We also prove that the Glauber dynamics behaves locally like loopy BP. As a byproduct we obtain that the Glauber dynamics, after a short burn-in period, converges close to the BP fixed point, and this implies that the fixed point of loopy BP is a close approximation to the Gibbs distribution. Using these connections we establish that loopy BP quickly converges to the Gibbs distribution when the girth $\geq 6$ and $\lambda<\lambda_c(\Delta)$.

This paper presents a new side channel that affects mixed-signal chips used in widespread wireless communication protocols, such as Bluetooth and WiFi. This increasingly common type of chip includes the radio transceiver along with digital logic on the same integrated circuit. In such systems, the radio transmitter may unintentionally broadcast sensitive information from hardware cryptographic components or software executing on the CPU. The well-known electromagnetic (EM) leakage from digital logic is inadvertently mixed with the radio carrier, which is amplified and then transmitted by the antenna. We call the resulting leak screaming channels. Attacks exploiting such a side channel may succeed over a much longer distance than attacks exploiting usual EM side channels. The root of the problem is that mixed-signal chips include both digital circuits and analog circuits on the same silicon die in close physical proximity. While processing data, the digital circuits on these chips generate noise, which can be picked up by noise-sensitive analog radio components, ultimately leading to leakage of sensitive information. We investigate the physical reasons behind the channel, we measure it on several popular devices from different vendors (including Nordic Semiconductor nRF52832, and Qualcomm Atheros AR9271), and we demonstrate a complete key recovery attack against the nRF52832 chip. In particular, we retrieve the full key from the AES-128 implementation in tinyAES at a distance of 10 m using template attacks. Additionally, we recover the key used by the AES-128 implementation in mbedTLS at a distance of 1 m with a correlation attack. Screaming channel attacks change the threat models of devices with mixed-signal chips, as those devices are now vulnerable from a distance. More specifically, we argue that protections against side channels (such as masking or hiding) need to be used on this class of devices. Finally, chips implementing other widespread protocols (e.g., 4G/LTE, RFID) need to be inspected to determine whether they are vulnerable to screaming channel attacks.

Energy is often the most constrained resource in networks of batterypowered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true energy usage, we define energy complexity to be the number of time slots a device transmits/listens; idle time and computation are free.

We study the mixing properties of the single-site Markov chain known as the Glauber dynamics for sampling k-colorings of a sparse random graph G(n, d/n) for constant d. The best known rapid mixing results for general graphs are in terms of the maximum degree Δ of the input graph G and hold when k > 11Δ/6 for all G. Improved results hold when k > αΔ for graphs with girth ≥ 5 and Δ sufficiently large where α ≈ 1.7632 … is the root of α = exp(1/α); further improvements on the constant α hold with stronger girth and maximum degree assumptions. For sparse random graphs the maximum degree is a function of n and the goal is to obtain results in terms of the expected degree d. The following rapid mixing results for G(n,d/n) hold with high probability over the choice of the random graph for sufficiently large constant d. Mossel and Sly (2009) proved rapid mixing for constant k, and Efthymiou (2014) improved this to k linear in d. The condition was improved to k > 3d by Yin and Zhang (2016) using non-MCMC methods. Here we prove rapid mixing when k > αd where α ≈ 1.7632 … is the same constant as above. Moreover we obtain O(n3) mixing time of the Glauber dynamics, while in previous rapid mixing results the exponent was an increasing function in d. Our proof analyzes an appropriately defined block dynamics to “hide” high-degree vertices. One new aspect in our improved approach is utilizing so-called local uniformity properties for the analysis of block dynamics. To analyze the “burn-in” phase we prove a concentration inequality for the number of disagreements propagating in large blocks.

We study the hard-core (gas) model defined on independent sets of an input graph where the independent sets are weighted by a parameter (aka fugacity) λ > 0. For constant Δ, previous work of Weitz (2006) established an FPTAS for the partition function for graphs of maximum degree Δ when λc(Δ). Sly (2010) showed that there is no FPRAS, unless NP=RP, when λ > λc(Δ). The threshold λc(Δ) is the critical point for the statistical physics phase transition for uniqueness/non-uniqueness on the infinite Δ-regular tree. The running time of Weitz's algorithm is exponential in log Δ. Here we present an FPRAS for the partition function whose running time is O* (n2). We analyze the simple single-site Markov chain known as the Glauber dynamics for sampling from the associated Gibbs distribution. We prove there exists a constant Δ0such that for all graphs with maximum degree Δ > Δ0and girth > 7 (i.e., no cycles of length ≤ 6), the mixing time of the Glauber dynamics is O(nlog n) when λc(Δ). Our work complements that of Weitz which applies for small constant Δ whereas our work applies for all Δ at least a sufficiently large constant Δ0(this includes Δ depending on n = IVI). Our proof utilizes loopy BP (belief propagation) which is a widely-used algorithm for inference in graphical models. A novel aspect of our work is using the principal eigenvector for the BP operator to design a distance function which contracts in expectation for pairs of states that behave like the BP fixed point. We also prove that the Glauber dynamics behaves locally like loopy BP. As a byproduct we obtain that the Glauber dynamics, after a short burn-in period, converges close to the BP fixed point, and this implies that the fixed point of loopy BP is a close approximation to the Gibbs distribution. Using these connections we establish that loopy BP quickly converges to the Gibbs distribution when the girth ≥ 6 and λc(Δ).

Robust Ad-hoc Sensor Routing (RASeR) is a novel protocol for data routing in mobile wireless sensor networks (MWSNs). It is designed to cope with the demanding requirements of emerging technologies, which require the reliable and low-latency delivery of packets in highly mobile conditions. RASeR uses blind forwarding, which is facilitated by a novel method of gradient maintenance. The problem of maintaining a gradient field in a changing topology, without flooding, is solved by using a global time division multiple access MAC. Furthermore, it is enhanced with the additional options of a supersede mode, to aid time-critical applications, reverse flooding, to allow sink-to-sensor commands and energy saving sleep cycles to reduce power consumption. Analytical expressions are derived and verified by simulation. RASeR is compared with the state-of-the-art MWSN routing protocols, PHASeR and MACRO, as well as the MANET protocols, AODV and OLSR. The results indicate that RASeR is a high performance protocol, which shows improvements over PHASeR, MACRO, AODV and OLSR. Tested over varying levels of mobility, scalability and traffic, the simulations yield near perfect PDR in many scenarios, as well as a low end-to-end delay, high throughput, low overhead and low energy consumption. The robustness of this protocol and its consistent reliability, low latency and additional features, makes it highly suitable to a wide number of applications. It is specifically applicable to highly mobile situations with a fixed number of nodes and small payloads.

This paper presents a novel multihop routing protocol for mobile wireless sensor networks called PHASeR (Proactive Highly Ambulatory Sensor Routing). The proposed protocol uses a simple hop-count metric to enable the dynamic and robust routing of data towards the sink in mobile environments. It is motivated by the application of radiation mapping by unmanned vehicles, which requires the reliable and timely delivery of regular measurements to the sink. PHASeR maintains a gradient metric in mobile environments by using a global TDMA MAC layer. It also uses the technique of blind forwarding to pass messages through the network in a multipath manner. PHASeR is analysed mathematically based on packet delivery ratio , average packet delay , throughput and overhead. It is then simulated with varying mobility, scalability and traffic loads. The protocol gives good results over all measures, which suggests that it may also be suitable for a wider array of emerging applications.

Nonnegative Least Squares (NNLS) is a general form for many important problems. We consider a special case of NNLS where the input is nonnegative. It is called Totally Nonnegative Least Squares (TNNLS) in the literature. We show a reduction of TNNLS to a single class Support Vector Machine (SVM), thus relating the sparsity of a TNNLS solution to the sparsity of supports in a SVM. This allows us to apply any SVM solver to the TNNLS problem. We get an order of magnitude improvement in running time by first obtaining a smaller version of our original problem with the same solution using a fast approximate SVM solver. Second, we use an exact NNLS solver to obtain the solution. We present experimental evidence that this approach improves the performance of state-of-the-art NNLS solvers by applying it to both randomly generated problems as well as to real datasets, calculating radiation therapy dosages for cancer patients.

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, 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 to each such change by quick "repairs," which consist of adding or deleting a small number of edges.

We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, not all keywords should be sold to the highest bidder. We assume that the sequence of keywords (or equivalently, of bids) is revealed on-line. Our concern will be the competitive ratio for this problem versus the off-line optimum.

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that the following process continues for up to n rounds where n is the total number of nodes initially in the network: the adversary deletesan arbitrary node from the network, then the network responds by quickly adding a small number of new edges.

In the online linear optimization problem, a learner must choose, in each round, a decision from a set D ⊂ Rn in order to minimize an (unknown and chang- ing) linear cost function. We present sharp rates of convergence (with respect to additive regret) for both the full information setting (where the cost function is revealed at the end of each round) and the bandit setting (where only the scalar cost incurred is revealed). In particular, this paper is concerned with the price of bandit information, by which we mean the ratio of the best achievable regret √ in the bandit setting to that in the full-information setting. For the full informa- tion case, the upper bound on the regret is O∗( nT ), where n is the ambient √ dimension and T is the time horizon. For the bandit case, we present an algorithm which achieves O∗(n3/2 T ) regret — all previous (nontrivial) bounds here were O(poly(n)T 2/3) or worse. It is striking that the convergence rate for the bandit setting is only a factor of n worse than in the full information case — in stark √ contrast to the K-arm bandit setting, where the gap in the dependence on K is T log K). We also present lower bounds showing that exponential ( this gap is at least n, which we conjecture to be the correct order. The bandit algorithm we present can be implemented efficiently in special cases of particular interest, such as path planning and Markov Decision Problems.

We consider a model for sequential online decision-making by many diverse agents. On each day, each agent makes a decision, and pays a penalty if it is a mistake. Obviously, it would be good for agents to avoid repeating the same mistakes made by other agents; however, difficulty may arise when some agents disagree over what constitutes a mistake, perhaps maliciously.

We study Markov chains for randomly sampling k-colorings of a graph with maximum degree δ. Our main result is a polynomial upper bound on the mixing time of the single-site update chain knownas the Glauber dynamics for planar graphs when k=Ω(δ/logδ). Our results can be partially extended to the more general case where the maximum eigenvalue of the adjacency matrix of the graphis at most δ1-e, for fixed e > 0.The main challenge when k ≤ δ + 1 is the possibility of frozen vertices, that is, vertices for which only one coloris possible, conditioned on the colors of its neighbors. Indeed, when δ = O(1), even a typical coloring canhave a constant fraction of the vertices frozen.Our proofs rely on recent advances in techniquesfor bounding mixing time using local uniformity properties.

Spin systems are a general way to describe local interactions between nodes in a graph. In statistical mechanics, spin systems are often used as a model for physical systems. In computer science, they comprise an important class of families of combinatorial objects, for which approximate counting and sampling algorithms remain an elusive goal. The Dobrushin condition states that every row sum of the "influence matrix" for a spin system is less than 1 - epsiv, where epsiv > 0. This criterion implies rapid convergence (O(n log n) mixing time) of the single-site (Glauber) dynamics for a spin system, as well as uniqueness of the Gibbs measure. The dual criterion that every column sum of the influence matrix is less than 1 - epsiv has also been shown to imply the same conclusions. We examine a common generalization of these conditions, namely that the maximum eigenvalue of the influence matrix is less than 1 epsiv. Our main result is that this criterion implies O(n log n) mixing time for the Glauber dynamics. As applications, we consider the Ising model, hard-core lattice gas model, and graph colorings, relating the mixing time of the Glauber dynamics to the maximum eigenvalue for the adjacency matrix of the graph. For the special case of planar graphs, this leads to improved bounds on mixing time with quite simple proofs

We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least /spl Omega/(n log n), where it is the number of vertices. Our bound applies to the so-called "Glauber dynamics" that has been used extensively in algorithms for the Ising model, independent sets, graph colorings and other structures in computer science and statistical physics, and demonstrates that many of these algorithms are optimal up to constant factors within their class. Previously no super-linear lower bound for this class of algorithms was known. Though widely conjectured, such a bound had been proved previously only in very restricted circumstances, such as for the empty graph and the path. We also show that the assumption of bounded degree is necessary by giving a family of dynamics on graphs of unbounded degree with mixing time O(n).

We introduce a reduction-based model for analyzing supervised learning tasks. We use this model to devise a new reduction from multi-class cost-sensitive classification to binary classification with the following guarantee: If the learned binary classifier has error rate at most ε then the cost-sensitive classifier has cost at most 2ε times the expected sum of costs of all possible lables. Since cost-sensitive classification can embed any bounded loss finite choice supervised learning task, this result shows that any such task can be solved using a binary classification oracle. Finally, we present experimental results showing that our new reduction outperforms existing algorithms for multi-class cost-sensitive learning.

We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling (proper) k-colorings of an input graph G on n vertices with maximum degree /spl Delta/ and girth g. We prove the Glauber dynamics is close to the uniform distribution after O(n log n) steps whenever k > (1 + /spl epsiv/)/spl Delta/, for all /spl epsiv/ > 0, assuming g /spl ges/ 9 and /spl Delta/ = /spl Omega/(log n). The best previously known bounds were k > 11/spl Delta//6 for general graphs, and k > 1.489/spl Delta/ for graphs satisfying girth and maximum degree requirements. Our proof relies on the construction and analysis of a non-Markovian coupling. This appears to be the first application of a non-Markovian coupling to substantially improve upon known results.

We improve rapid mixing results for the simple Glauber dynamics designed to generate a random k-coloring of a bounded-degree graph.Let G be a graph with maximum degree Δ = Ω(log n), and girth ≥ 5. We prove that if k > Α Δ, where Α ≈ 1.763 then Glauber dynamics has mixing time O(n log n). If girth(G) ≥ 6 and k > Β Δ, where Β ≈ 1.489 then Glauber dynamics has mixing time O(n log n). This improves a recent result of Molloy, who proved the same conclusion under the stronger assumptions that Δ=Ω(log n) and girth Ω(log Δ). Our work suggests that rapid mixing results for high girth and degree graphs may extend to general graphs.Analogous results hold for random graphs of average degree up to n¼, compared with polylog(n), which was the best previously known.Some of our proofs rely on a new Chernoff-Hoeffding type bound, which only requires the random variables to be well-behaved with high probability. This tail inequality may be of independent interest.

We generalize the multiparty communication model of Chandra, Furot, nnd Lipton (1983) to functions with b-bit output (6 = 1 in (he CFL model), We allow the parties to receive up to b -1 bits of information from an all-powerful benevolent Helper who can see all lhc Input.WC construct families of explicit functions for which fl(n/c") bits of communication are required to find the "missing bit," where n ia the length of each player's input and H is the number of players, This extends the results of Babal, Nisan, Szegedy (1992), As a consequence we settle the old problem of separatlng the one-wny vs. multiround communication complexities (in the CFL sense) for h 5 (1 -6) log 9~ players, extending a result of Nionn and Wigdcrson (1991) who demonstrated this separation for 12 z 3 players.As a by-product we obtain S2(n/ck) lower bounds for the multiparty complexity (in the CFL sense) of new families of explicit boolean functions (not derivable from BNS).The proofs exploit the interplay between two new theories of multicolor discrepancy; discrete Fourier analysis is the basic tool.We nlao include a previously unpublished lower bound by A. Wigdernon regarding the one-way complexity of the 3-party pointer jumping function,