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Lower bounds for the minimum linear arrangement of a graph

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>1/08/2010
<mark>Journal</mark>Electronic Notes in Discrete Mathematics
Number of pages7
Pages (from-to)843-849
Publication StatusPublished
<mark>Original language</mark>English


Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which 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.