Computing Directed Steiner Path Covers

TL;DR

This paper presents a linear time algorithm for computing minimum Steiner path covers and Hamiltonian paths in directed co-graphs, with applications in optimizing manufacturing processes.

Contribution

It introduces the first linear time algorithm for the directed Steiner path cover and Hamiltonian path problems on directed co-graphs, and provides integer programming formulations.

Findings

Linear time algorithm for Steiner path cover on directed co-graphs

Linear time computation of optimal directed Steiner paths if they exist

Integer programming models for related problems

Abstract

In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph G=(V,E) and a subset T of V of so-called terminal vertices, the problem is to find a minimum number of vertex-disjoint simple directed paths, which contain all terminal vertices and a minimum number of non-terminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute in linear time a minimum Steiner path cover for directed co-graphs. This leads to a linear time computation of an optimal directed Steiner path on directed co-graphs, if it exists. Since the Steiner path problem generalizes the Hamiltonian path problem, our results imply the first linear time algorithm for the directed Hamiltonian path problem on directed co-graphs. We also give binary integer programs for the (directed) Hamiltonian path problem, for the (directed) Steiner path problem, and for the (directed) Steiner path cover problem. These integer programs can be used to minimize change-over times in pick-and-place machines used by companies in electronic industry.