We consider two models of computation: centralized localalgorithms and localdistributedalgorithms. algorithms in one model are adapted to the other model to obtain improved algorithms. distributed vertex coloring i...
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We consider two models of computation: centralized localalgorithms and localdistributedalgorithms. algorithms in one model are adapted to the other model to obtain improved algorithms. distributed vertex coloring is employed to design improved centralized localalgorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in log* n, where n is the number of vertices of the input graph. The recursive centralized local improvement technique by Nguyen and Onak (FOCS 2008) is employed to obtain a distributed approximation scheme for maximum (weighted) matching. (C) 2018 Elsevier Inc. All rights reserved.
The paper tackles the power of randomization in the context of localdistributed computing by analyzing the ability to "boost" the success probability of deciding a distributed language using a Monte-Carlo a...
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The paper tackles the power of randomization in the context of localdistributed computing by analyzing the ability to "boost" the success probability of deciding a distributed language using a Monte-Carlo algorithm. We prove that, in many cases, the ability to increase the success probability for deciding distributed languages is rather limited. This contrasts with the sequential computing setting where boosting can systematically be achieved by repeating the randomized execution.
We present deterministic distributedalgorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is...
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ISBN:
(纸本)9781450329286
We present deterministic distributedalgorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1- epsilon) times the optimal in Delta(O(1/epsilon)) + O (1/epsilon(2))center dot log*(n) rounds where n is the number of vertices in the graph and Delta is the maximum degree. Our algorithm for the edge weighted case computes a matching whose weight is at least (1- epsilon) times the optimal in log(min{1/w(min),n/epsilon})(O(1/epsilon)) (Delta(O(1/epsilon))+log*(n)) rounds for edge-weights in [w(min), 1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie (SPAA 2008). For the unweighted case they give a randomized (1- epsilon)-approximation algorithm that runs in O((log(n))/epsilon(3)) rounds. For the weighted case they give a randomized (1/2- epsilon)-approximation algorithm that runs in O(log(epsilon(-1)) center dot log(n)) rounds. Hence, our results improve on the previous ones when the parameters Delta, epsilon and w(min), are constants (where we reduce the number of runs from O(log(n)) to O(log*(n))), and more generally when Delta, 1/epsilon and 1/w(min) are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.
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