Decorous Lower Bounds for Minimum Linear Arrangement

Authors:
Alberto Caprara;Adam N. Letchford;Juan-José Salazar-González
Affiliations:
Dipartimento di Elettronica, Informatica e Sistemistica, Università di Bologna, I-40136 Bologna, Italy;Department of Management Science, Lancaster University, Lancaster LA1 4YX, United Kingdom;Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, E-38271 La Laguna, Tenerife, Spain
Venue:
INFORMS Journal on Computing
Year:
2011

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Abstract

Minimum linear arrangement is a classical basic combinatorial optimization problem from the 1960s that turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best-known solution value often has one more digit than the best-known lower bound value. In this paper, we propose a linear programming-based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best-known solutions are indeed not far from optimal for most of the benchmark instances.