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Decorous lower bounds for minimum linear arrangement. (English) Zbl 1243.90185
Summary: 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.

90C27 Combinatorial optimization
05C62 Graph representations (geometric and intersection representations, etc.)
05C85 Graph algorithms (graph-theoretic aspects)
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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