A synthesis on partition refinement: A useful routine for strings, graphs, boolean matrices and automata

Abstract

Partition refinement techniques are used in many algorithms. This tool allows efficient computation of equivalence relations and is somehow dual to union-find algorithms. The goal of this paper is to propose a single routine to quickly implement all these already known algorithms and to solve a large class of potentially new problems. Our framework yields to a unique scheme for correctness proofs and complexity analysis. Various examples are presented to show the different ways of using this routine. © 1998 Springer-Verlag.