An efficient implicit OBDD-based algorithm for maximal matchings

Abstract

The maximal matching problem, i.e., the computation of a matching that is not a proper subset of another matching, is a fundamental optimization problem and algorithms for maximal matchings have been used as submodules for problems like maximal node-disjoint paths or maximum flow. Since in some applications graphs become larger and larger, a research branch has emerged which is concerned with the design and analysis of implicit algorithms for classical graph problems. Input graphs are given as characteristic Boolean functions of their edge sets and problems have to be solved by functional operations. As OBDDs, which are closely related to deterministic finite automata, are a well-known data structure for Boolean functions, OBDD-based algorithms are used as a heuristic approach to handle very large graphs. Here, an implicit OBDD-based maximal matching algorithm is presented that uses only a polylogarithmic number of functional operations with respect to the number of vertices of the input graph. © 2012 Springer-Verlag.