An improved algorithm for transitive closure on acyclic digraphs

Abstract

In [6] Geralcikova, Koubek describe an algorithm for finding the transitive closure of an acyclic digraph G with worst case runtime O(n·ered), where n is the number of nodes and ered is the number of edges in the transitive reduction of G. We present an improvement on their algorithm which runs in worst case time O(k·ered) and space O(n·k), where k is the width of a chain decomposition. For the expected values in the Gn,p model of a random acyclic digraph with 0 < p < 1 we have: (Formula pressented.).