Strong lower bounds for the prize collecting Steiner problem in graphs

Authors:
Abilio Lucena;Mauricio G. C. Resende
Affiliations:
Departamento de Administração, Universidade Federal do Rio de Janeiro, Av. Pasteur 250, 22290-240 Rio de Janeiro, RJ, Brazil;AT&T Labs Research, Internet and Network Systems Research Center, 180 Park Avenue, Room C241, Florham Park, NJ
Venue:
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Year:
2004

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Abstract

In this paper, we present an integer programming formulation of the prize collecting Steiner problem in graphs (PCSPG) and describe an algorithm to obtain lower bounds for the problem. The algorithm is based on polyhedral cutting planes and is initiated with tests that attempt to reduce the size of the input graph. Computational experiments were carried out to evaluate the strength of the formulation through its linear programming relaxation. On 96 out of the 114 instances tested, integer solutions were found (thus generating optimal PCSPG solutions).