Mathematical Programming Computation, Volume 3, Issue 3, August 2011
Optimal linear arrangements using betweenness variables
Alberto Caprara, Marcus Oswald, Gerhard Reinelt, Robert Schwarz, Emiliano Traversi
We solve for the first time to proven optimality the small instances in the classical literature benchmark of Minimum Linear Arrangement. This is achieved by formulating the problem as an ILP in a somehow unintuitive way, using variables expressing the fact that a vertex is between two other adjacent vertices in the arrangement. Using (only) these variables appears to be the key idea of the approach. Indeed, with these variables already the use of very simple constraints leads to good results, which can however be improvedwith amore detailed study of the underlying polytope.
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