Adjacency Variables Formulation for the Minimum Linear Arrangement Problem
We present a new integer linear formulation using \(O(n^2)\) variables, called adjacency variables, to solve the Minimum Linear Arrangement problem (MinLA). We give a couple of valid equalities and inequalities for this formulation, some of them deriving from on a new general partitioning approach that is not limited to our formulation. We numerically tested the lower bound provided by the linear relaxation using instances of the matrix market library. Our results are compare with the best known lower bounds, in terms of quality, as well computing times.
KeywordsMinimum linear arrangement problem Integer programming Graph partitioning Cutting plane algorithms
This work was financially supported by the region of Haute- Normandie (France) and the European Union. This support is gratefully acknowledged.
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