A network approach for specially structured linear programs arising in 0-1 quadratic optimization

Authors:
Warren P. Adams;Paul T. Hadavas
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC, USA;Department of Mathematics, Armstrong Atlantic State University, Savannah, GA, USA
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

Reformulation techniques are commonly used to transform 0-1 quadratic problems into equivalent, mixed 0-1 linear programs. A classical strategy is to replace each quadratic term with a continuous variable and to enforce, for each such product, four linear inequalities that ensure the continuous variable equals the associated product. By employing a transformation of variables, we show how such inequalities give rise to a network structure, so that the continuous relaxations can be readily solved. This work unifies and extends related results for the vertex packing problem and relatives, and roof duality.