TY - JOUR

T1 - Decorous lower bounds for minimum linear arrangement

AU - Caprara, A

AU - Letchford, A N

AU - Salazar, J J

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - combinatorial optimisation

KW - cutting planes

KW - graph layout problems

U2 - 10.1287/ijoc.1100.0390

DO - 10.1287/ijoc.1100.0390

M3 - Journal article

VL - 23

SP - 26

EP - 40

JO - INFORMS Journal on Computing

JF - INFORMS Journal on Computing

SN - 1526-5528

IS - 1

ER -