Maximum matchings in random bipartite graphs and the space utilization of Cuckoo Hash tables

Authors:
Alan Frieze;Páll Melsted
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 and Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Ic ...
Venue:
Random Structures & Algorithms
Year:
2012

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Abstract

We study the the following question in Random Graphs. We are given two disjoint sets L,R with |L| = n and |R| = m. We construct a random graph G by allowing each x∈L to choose d random neighbours in R. The question discussed is as to the size μ(G) of the largest matching in G. When considered in the context of Cuckoo Hashing, one key question is as to when is μ(G) = n whp? We answer this question exactly when d is at least three. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.