Randomized greedy matching. II

Authors:
Jonathan Aronson;Martin Dyer;Alan Frieze;Stephen Suen
Affiliations:
Department of Mathematics, Carnegie‐Mellon University, Pittsburgh, PA 15213;Department of Mathematics, Carnegie‐Mellon University, Pittsburgh, PA 15213;Department of Mathematics, Carnegie‐Mellon University, Pittsburgh, PA 15213;Department of Mathematics, Carnegie‐Mellon University, Pittsburgh, PA 15213
Venue:
Random Structures & Algorithms
Year:
1995

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Abstract

We consider the following randomized algorithm for finding a matching M in an arbitrary graph G = (V, E). Repeatedly, choose a random vertex u, then a random neighbour v of u. Add edge {u, v} to M and delete vertices u, v from G along with any vertices that become isolated. Our main result is that there exists a positive constant ϵ such that the expected ratio of the size of the matching produced to the size of largest matching in G is at least 0.5 + ϵ. We obtain stronger results for sparse graphs and trees and consider extensions to hypergraphs. © 1995 Wiley Periodicals, Inc.