Results 1  10
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44
An online algorithm for maximizing submodular functions
, 2007
"... We present an algorithm for solving a broad class of online resource allocation jobs arrive one at a time, and one can complete the jobs by investing time in a number of abstract activities, according to some schedule. We assume that the fraction of jobs completed by a schedule is a monotone, submod ..."
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Cited by 55 (12 self)
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We present an algorithm for solving a broad class of online resource allocation jobs arrive one at a time, and one can complete the jobs by investing time in a number of abstract activities, according to some schedule. We assume that the fraction of jobs completed by a schedule is a monotone, submodular function of a set of pairs (v, τ), where τ is the time invested in activity v. Under this assumption, our online algorithm performs nearoptimally according to two natural metrics: (i) the fraction of jobs completed within time T, for some fixed deadline T> 0, and (ii) the average time required to complete each job. We evaluate our algorithm experimentally by using it to learn, online, a schedule for allocating CPU time among solvers entered in the 2007 SAT solver competition. 1
Delay reduction via lagrange multipliers in stochastic network optimization
 In Proc. of the 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 2009
, 2009
"... Abstract—In this paper, we consider the problem of reducing network delay in stochastic network utility optimization problems. We start by studying the recently proposed quadratic Lyapunov function based algorithms (QLA). We show that for every stochastic problem, there is a corresponding determinis ..."
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Cited by 29 (16 self)
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Abstract—In this paper, we consider the problem of reducing network delay in stochastic network utility optimization problems. We start by studying the recently proposed quadratic Lyapunov function based algorithms (QLA). We show that for every stochastic problem, there is a corresponding deterministic problem, whose dual optimal solution “exponentially attracts” the network backlog process under QLA. In particular, the probability that the backlog vector under QLA deviates from the attractor is exponentially decreasing in their Euclidean distance. This suggests that one can roughly “subtract out ” a Lagrange multiplier from the system induced by QLA. We thus develop a family of Fast Quadratic Lyapunov based Algorithms (FQLA) that achieve an [O(1/V), O(log 2 (V))] performancedelay tradeoff. These results highlight the “network gravity ” role of Lagrange Multipliers in network scheduling. This role can be viewed as the counterpart of the “shadow price ” role of Lagrange Multipliers in flow regulation for classic flowbased network problems.
Broadcasting vs. mixing and information dissemination on Cayley graphs
 In 24th Int. Symp. on Theor. Aspects of Computer Science (STACS
, 2007
"... Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succe ..."
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Cited by 18 (6 self)
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Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. First, we consider the relationship between randomized broadcasting and random walks on graphs. In particular, we prove that the runtime of the algorithm described above is upper bounded by the corresponding mixing time, up to a logarithmic factor. One key ingredient of our proofs is the analysis of a continuoustype version of the afore mentioned algorithm, which might be of independent interest. Then, we introduce a general class of Cayley graphs, including (among others) Star graphs, Transposition graphs, and Pancake graphs. We show that randomized broadcasting has optimal runtime on all graphs belonging to this class. Finally, we develop a new proof technique by combining martingale tail estimates with combinatorial methods. Using this approach, we show the optimality of our algorithm on another Cayley graph and obtain new knowledge about the runtime distribution on several Cayley graphs. 1
Revisiting the Efficiency of Malicious TwoParty Computation
 In Eurocrypt ’07, SpringerVerlag (LNCS 4515
, 2006
"... In a recent paper Mohassel and Franklin study the e#ciency of secure twoparty computation in the presence of malicious behavior. Their aim is to make classical solutions to this problem, such as zeroknowledge compilation, more practical. The authors provide several schemes which are the most e# ..."
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Cited by 16 (0 self)
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In a recent paper Mohassel and Franklin study the e#ciency of secure twoparty computation in the presence of malicious behavior. Their aim is to make classical solutions to this problem, such as zeroknowledge compilation, more practical. The authors provide several schemes which are the most e#cient to date. We propose a modification to their main scheme using expanders.
Reconstruction for colorings on trees
, 2008
"... Consider kcolorings of the complete tree of depth ℓ and branching factor ∆. If we fix the coloring of the leaves, for what range of k is the root uniformly distributed over all k colors (in the limit ℓ → ∞)? This corresponds to the threshold for uniqueness of the infinitevolume Gibbs measure. It i ..."
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Cited by 12 (5 self)
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Consider kcolorings of the complete tree of depth ℓ and branching factor ∆. If we fix the coloring of the leaves, for what range of k is the root uniformly distributed over all k colors (in the limit ℓ → ∞)? This corresponds to the threshold for uniqueness of the infinitevolume Gibbs measure. It is straightforward to show the existence of colorings of the leaves which “freeze ” the entire tree when k ≤ ∆ + 1. For k ≥ ∆ + 2, Jonasson proved the root is “unbiased ” for any fixed coloring of the leaves and thus the Gibbs measure is unique. What happens for a typical coloring of the leaves? When the leaves have a nonvanishing influence on the root in expectation, over random colorings of the leaves, reconstruction is said to hold. Nonreconstruction is equivalent to extremality of the Gibbs measure. When k < ∆ / ln ∆, it is straightforward to show that reconstruction is possible (and hence the measure is not extremal). We prove that for C> 2 and k = C∆ / ln ∆, nonreconstruction holds, i.e., the Gibbs measure is extremal. We prove a strong form of extremality: with high probability over the colorings of the leaves the influence at the root decays exponentially fast with the depth of the tree. These are the first results coming close to the threshold for extremality for colorings. Extremality on trees and random graphs has received considerable attention recently since it may have connections to the efficiency of local algorithms.
Achieving the empirical capacity using feedback  part II: General models,” in preparation
"... We address the problem of universal communications over an unknown channel with an instantaneous noiseless feedback, and show how rates corresponding to the empirical behavior of the channel can be attained, although no rate can be guaranteed in advance. First, we consider a discrete moduloadditive ..."
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Cited by 11 (4 self)
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We address the problem of universal communications over an unknown channel with an instantaneous noiseless feedback, and show how rates corresponding to the empirical behavior of the channel can be attained, although no rate can be guaranteed in advance. First, we consider a discrete moduloadditive channel with alphabet X, where the noise sequence Z n is arbitrary and unknown and may causally depend on the transmitted and received sequences and on the encoder’s message, possibly in an adversarial fashion. Although the classical capacity of this channel is zero, we show that rates approaching the empirical capacity log X  − Hemp(Z n) can be universally attained, where Hemp(Z n) is the empirical entropy of Z n. For the more general setting where the channel can map its input to an output in an arbitrary unknown fashion subject only to causality, we model the empirical channel actions as the moduloaddition of a realized noise sequence, and show that the same result applies if common randomness is available. The results are proved constructively, by providing a simple sequential transmission scheme approaching the empirical capacity. In part II of this work we demonstrate how even higher rates can be attained by using more elaborate models for channel actions, and by utilizing possible empirical dependencies in its behavior.
Stochastic belief propagation: A lowcomplexity alternative to the sumproduct algorithms
 COMPUTING RESEARCH REPOSITORY
, 2011
"... The belief propagation (BP) or sumproduct algorithm is a widelyused messagepassing method for computing marginal distributions in graphical models. At the core of the BP message updates, when applied to a graphical model involving discrete variables with pairwise interactions, lies a matrixvect ..."
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Cited by 8 (4 self)
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The belief propagation (BP) or sumproduct algorithm is a widelyused messagepassing method for computing marginal distributions in graphical models. At the core of the BP message updates, when applied to a graphical model involving discrete variables with pairwise interactions, lies a matrixvector product with complexity that is quadratic in the state dimension d, and requires transmission of a (d − 1)dimensional vector of real numbers (messages) to its neighbors. Since various applications involve very large state dimensions, such computation and communication complexities can be prohibitively complex. In this paper, we propose a lowcomplexity variant of BP, referred to as stochastic belief propagation (SBP). As suggested by the name, it is an adaptively randomized version of the BP message updates in which each node passes randomly chosen information to each of its neighbors. The SBP message updates reduce the computational complexity (per iteration) from quadratic to linear in d, without assuming any particular structure of the potentials, and also reduce the communication complexity significantly, requiring only log 2d bits transmission per edge. Moreover, we establish a number of theoretical guarantees for the performance of SBP, showing that it converges almost surely to the BP fixed point for any treestructured graph, and for any graph with cycles satisfying a contractivity condition. In addition, for these graphical models, we provide nonasymptotic upper bounds on the convergence rate, showing that the ℓ ∞ norm of the error vector decays no slower than O ( 1 / √ t) with the number of iterations t on trees and the normalized meansquared error decays as O ( 1/t) for general graphs. This analysis, also supported by experimental results, shows that SBP can provably yield reductions in computational and communication complexities for various classes of graphical models.
Concentration and Moment Inequalities for Polynomials of Independent Random Variables
"... In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many others. We apply our method to derive general concentration inequa ..."
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Cited by 8 (2 self)
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In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many others. We apply our method to derive general concentration inequalities for polynomials of independent random variables. We show that our method implies concentration inequalities for some previously open problems, e.g. permanent of random symmetric matrices. We show that our concentration inequality is stronger than the wellknownconcentration inequalityduetoKimandVu[29]. The main advantage of our method in comparison with the existing ones is a wide range of random variables we can handle and bounds for previously intractable regimes of high degree polynomials and small expectations. On the negative side we show that even for boolean random variables each term in our concentration inequality is tight.
Sleeping Experts and Bandits with Stochastic Action Availability and Adversarial Rewards
 In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, number 5
, 2009
"... We consider the problem of selecting actions in order to maximize rewards chosen by an adversary, where the set of actions available on any given round is selected stochastically. We present the first polynomialtime noregret algorithm for this setting. In the fullobservation (experts) version of ..."
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Cited by 5 (1 self)
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We consider the problem of selecting actions in order to maximize rewards chosen by an adversary, where the set of actions available on any given round is selected stochastically. We present the first polynomialtime noregret algorithm for this setting. In the fullobservation (experts) version of the problem, we present an exponentialweights algorithm that achieves regret O ( √ T log n), which is the best possible. For the bandit setting (where the algorithm only observes the reward of the action selected), we present a noregret algorithm based on followtheperturbedleader. This algorithm runs in polynomial time, unlike the EXP4 algorithm which can also be applied to this setting. Our algorithm has the interesting interpretation of solving a geometric experts problem where the actual embedding is never explicitly constructed. We argue that this adversarialreward, stochasticavailability formulation is important in practice, as assuming stationary stochastic rewards is unrealistic in many domains. 1