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A mixed 0-1 linear programming formulation for the exact solution of the minimum linear arrangement problem

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Abstract

We are concerned with the exact solution of a graph optimization problem known as minimum linear arrangement (MinLA). Define the length of each edge of a graph with respect to a linear ordering of the graph vertices. Then, the MinLA problem asks for a vertex ordering that minimizes the sum of edge lengths. MinLA has several practical applications and is NP-Hard. We present a mixed 0-1 linear programming formulation of the problem, which led to fast optimal solutions for dense graphs of sizes up to n = 23.

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  1. Departamento de Informatica, Universidade Federal do Espirito Santo, Vitoria, ES, 29060-900, Brazil

    André R. S. Amaral

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  1. André R. S. Amaral
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Amaral, A.R.S. A mixed 0-1 linear programming formulation for the exact solution of the minimum linear arrangement problem. Optim Lett 3, 513–520 (2009). https://doi.org/10.1007/s11590-009-0130-0

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