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arXiv · 2011.06481

Communication Efficient Coresets for Maximum Matching

Michael Kapralov·Gilbert Maystre·Jakab Tardos
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Abstract

In this paper we revisit the problem of constructing randomized composable coresets for bipartite matching. In this problem the input graph is randomly partitioned across $k$ players, each of which sends a single message to a coordinator, who then must output a good approximation to the maximum matching in the input graph. Assadi and Khanna gave the first such coreset, achieving a $1/9$-approximation by having every player send a maximum matching, i.e. at most $n/2$ words per player. The approximation factor was improved to $1/3$ by Bernstein et al. In this paper, we show that the matching skeleton construction of Goel, Kapralov and Khanna, which is a carefully chosen (fractional) matching, is a randomized composable coreset that achieves a $1/2-o(1)$ approximation using at most $n-1$ words of communication per player. We also show an upper bound of $2/3+o(1)$ on the approximation ratio achieved by this coreset.

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Michael Kapralov, Gilbert Maystre, Jakab Tardos. 2020-11-12. Communication Efficient Coresets for Maximum Matching. https://arxiv.org/abs/2011.06481

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