Adapting Sequential Algorithms to the Distributed Setting
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In this paper we aim to define a robust family of sequential algorithms which can be easily adapted to the distributed setting. We then develop new tools to further enhance these algorithms, achieving state of the art results for fundamental problems. We define a simple class of greedy-like algorithms which we call orderless-local algorithms. We show that given a legal c-coloring of the graph, every algorithm in this family can be converted into a distributed algorithm running in O(c) communication rounds in the CONGEST model. We show that this family is indeed robust as both the method of conditional expectations and the unconstrained submodular maximization algorithm of Buchbinder et al. can be expressed as orderless-local algorithms for local utility functions --- Utility functions which have a strong local nature to them. We use the above algorithms as a base for new distributed approximation algorithms for three fundamental problems: Max k-Cut, Max-DiCut, Max 2-SAT and correlation clustering. We develop algorithms which have the same approximation guarantees as their sequential counterparts, up to an additive ϵ factor, while achieving an O(ϵ^-2Δ + ^* n) running time for deterministic algorithms and O(ϵ^-1) running time for randomized ones. This improves exponentially upon the currently best known algorithms.
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