Adjacency Variables Formulation for the Minimum Linear Arrangement Problem

  • Serigne GueyeEmail author
  • Sophie Michel
  • Mahdi Moeini
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 509)


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.


Minimum 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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Laboratoire d’Informatique d’Avignon (LIA)Avignon Cedex 9France
  2. 2.Laboratoire de Mathmatiques Appliques du Havre (LMAH)Le Havre CedexFrance
  3. 3.Centre de Recherche en Informatique de Lens (CRIL)Lens CedexFrance
  4. 4.Chair of Business Information Systems and Operations Research (BISOR)Technical University of KaiserslauternKaiserslauternGermany

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