Submodular Maximization Meets Streaming: Matchings, Matroids, and More

Abstract

AbstractWe study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This problem, which we call maximum submodular-function matching (MSM), is a natural generalization of maximum weight matching (MWM). We give two incomparable algorithms for this problem with space usage falling in the semi-streaming range—they store only O(n) edges, using O(nlogn) working memory—that achieve approximation ratios of 7.75 in a single pass and (3 + ε) in O(ε − 3) passes respectively. The operations of these algorithms mimic those of known MWM algorithms. We identify a general framework that allows this kind of adaptation to a broader setting of constrained submodular maximization. Note. A full version of this extended abstract [1] can be found online at the following URL: http://arxiv.org/abs/1309.2038 .KeywordsApproximation RatioSubmodular FunctionMaximum Weight MatchCompliant AlgorithmMaximum Cardinality MatchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.