Linear Ordering Based MIP Formulations for the Vertex Separation or Pathwidth Problem

Abstract

We consider the vertex separation problem in directed graphs G=(V,A) that has been shown to be equivalent to the pathwidth problem. Naturally, it is modeled as finding a linear order (permutation) of the vertices V such that its induced maximum vertex separation is minimum. Mixed-integer programs proposed so far construct linear orders using either position or set assignment variables. We prove that, for any directed graph, solving their linear programming relaxations yields a lower bound of zero on the true vertex separation number. We then present a new and compact mixed-integer program that sustains stronger lower bounds. It is based on true linear ordering variables and a slightly different perspective on the problem. An experimental evaluation of three formulations in total, each representing a different modeling scheme, displays their potentials and limitations when used to solve the problem to optimality

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Last time updated on 17/12/2017

This paper was published in computer science publication server.

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