Asymptotic analysis of an assignment problem arising in a distributed communications protocol

Abstract

Matchings for a random bipartite graph are considered. Each of the alpha M nodes on one side of the graph is directly connected to Q nodes chosen randomly and uniformly from among the M nodes on the other side of the graph. The size matchings found by two simple approximation algorithms, as well as the size of the maximum matching when Q=2, are asymptotically determined in the limit as Q tends to infinity with alpha fixed. The work is motivated by a distributed communications protocol for accessing a silent receiver. The theory of approximating slow Markov random walks by ordinary differential equations is used for the analysis.<>