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Strong lower bounds for the prize collecting Steiner problem in graphs

✍ Scribed by Abilio Lucena; Mauricio G.C Resende

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
260 KB
Volume
141
Category
Article
ISSN
0166-218X

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✦ Synopsis

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).

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In this paper, we study the Node Weighted Steiner Tree Problem (NSP). This problem is a generalization of the Steiner tree problem in the sense that vertex weights are considered. Given an undirected graph, the problem is to find a tree that spans a subset of the vertices and is such that the total