Theoretical and computational study of several linearisation techniques for binary quadratic problems

  • Fabio FuriniEmail author
  • Emiliano Traversi
Original Research


We perform a theoretical and computational study of the classical linearisation techniques (LT) and we propose a new LT for binary quadratic problems (BQPs). We discuss the relations between the linear programming (LP) relaxations of the considered LT for generic BQPs. We prove that for a specific class of BQP all the LTs have the same LP relaxation value. We also compare the LT computational performance for four different BQPs from the literature. We consider the Unconstrained BQP and the maximum cut of edge-weighted graphs and, in order to measure the effects of constraints on the computational performance, we also consider the quadratic extension of two classical combinatorial optimization problems, i.e., the knapsack and stable set problems.


Linearisation techniques Binary quadratic problems Max cut problem Quadratic knapsack problem Quadratic stable set problem 



Thanks are due to two anonymous referees for careful reading and useful comments.


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Authors and Affiliations

  1. 1.PSL, CNRS, LAMSADE UMR 7243Université Paris DauphineParis Cedex 16France
  2. 2.Laboratoire d’Informatique de Paris NordUniversité de Paris 13VilletaneuseFrance

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