Algorithms For Longest Chains In Pseudo- Transitive Graphs

Abstract

A directed acyclic graph G = (V, E) is pseudo-transitive with respect to a given subset of edges E1, if for any edge ab in E1 and any edge bc in E, we have ac in E. We give algorithms for computing longest chains and demonstrate geometric applications that unify and improves some important past results. (For specific applications see the introduction.)

The results in the paper had been announced in Elbe Sandstones Geometry Workshop, July 2001, Charles University, Prague, Czech Republic and DIMACS workshop on geometric graph theory, Rutgers University, NJ, 2002