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On the prize-collecting generalized minimum spanning tree problem

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Abstract

The prize-collecting generalized minimum spanning tree problem (PC-GMSTP), is a generalization of the generalized minimum spanning tree problem (GMSTP) and belongs to the hard core of \({\cal{NP}}\)-hard problems. We describe an exact exponential time algorithm for the problem, as well we present several mixed integer and integer programming formulations of the PC-GMSTP. Moreover, we establish relationships between the polytopes corresponding to their linear relaxations and present an efficient solution procedure that finds the optimal solution of the PC-GMSTP for graphs with up 240 nodes.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Sciences, North University of Baia Mare, Baia Mare, Romania

    P. C. Pop

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  1. P. C. Pop
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Correspondence to P. C. Pop.

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Pop, P.C. On the prize-collecting generalized minimum spanning tree problem. Ann Oper Res 150, 193–204 (2007). https://doi.org/10.1007/s10479-006-0153-1

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  • DOI: https://doi.org/10.1007/s10479-006-0153-1

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