On a binary distance model for the minimum linear arrangement problem
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- Reinelt, G. & Seitz, H. TOP (2014) 22: 384. doi:10.1007/s11750-012-0263-7
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The minimum linear arrangement problem consists of finding an embedding of the nodes of a graph on the line such that the sum of the resulting edge lengths is minimized. The problem is among the classical NP-hard optimization problems and there has been extensive research on exact and approximative algorithms. In this paper, we introduce a new model based on binary variables dijk that are equal to 1 if nodes i and j have distance k in the ordering. We analyze this model and point to connections and differences to a model using integer distance variables. Based on computational experiments, we argue that our model is worth further theoretical and practical investigation and that is has potentials yet to be examined.