Communication complexity of approximate maximum matching in the
message-passing model
release_bvjfnlx5mne7fo6df2nxpgbdom
by
Zengfeng Huang, Bozidar Radunovic, Milan Vojnovic, Qin Zhang
2017
Abstract
We consider the communication complexity of finding an approximate maximum
matching in a graph in a multi-party message-passing communication model. The
maximum matching problem is one of the most fundamental graph combinatorial
problems, with a variety of applications.
The input to the problem is a graph G that has n vertices and the set of
edges partitioned over k sites, and an approximation ratio parameter
α. The output is required to be a matching in G that has to be
reported by one of the sites, whose size is at least factor α of the
size of a maximum matching in G.
We show that the communication complexity of this problem is Ω(α^2
k n) information bits. This bound is shown to be tight up to a n
factor, by constructing an algorithm, establishing its correctness, and an
upper bound on the communication cost. The lower bound also applies to other
graph combinatorial problems in the message-passing communication model,
including max-flow and graph sparsification.
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