Distributed Maximum Matching in Bounded Degree Graphs release_i3ph7rit6vb2tbtekp5isrx3mi

by Guy Even, Moti Medina, Dana Ron

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2014  

Abstract

We present deterministic distributed algorithms 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-) times the optimal in Δ^O(1/) + O(1/^2) ·^*(n) rounds where n is the number of vertices in the graph and Δ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1-) times the optimal in ({1/,n/})^O(1/)·(Δ^O(1/)+^*(n)) rounds for edge-weights in [,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-)-approximation algorithm that runs in O(((n)) /^3) rounds. For the weighted case they give a randomized (1/2-)-approximation algorithm that runs in O((^-1) ·(n)) rounds. Hence, our results improve on the previous ones when the parameters Δ, and are constants (where we reduce the number of runs from O((n)) to O(^*(n))), and more generally when Δ, 1/ and 1/ are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.
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Date   2014-07-29
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arXiv  1407.7882v1
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