On the directed hop-constrained shortest path problem

Authors:
Geir Dahl;Luis Gouveia
Affiliations:
Department of Mathematics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway and Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway;DEIO-CIO, Faculdade de Ciências da Universidade de Lisboa, Bloco C/2-Campo Grande, Cidade Universitaria, 1700 Lisboa, Portugal
Venue:
Operations Research Letters
Year:
2004

Citing 3
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Abstract

In this paper we discuss valid inequalities for the directed hop-constrained shortest path problem. We give complete linear characterizations of the hop-constrained path polytope when the maximum number of hops is equal to 2 or 3. We also present a lifted version of the ''jump'' inequalities introduced by Dahl (Oper. Res. Lett. 25 (1999) 97) and show that this class of inequalities subsumes inequalities contained in the complete linear description for the case H=3 as well as a large class of facet defining inequalities for the case H=4. We use a minmax result by Robacker (Research Memorandum RM-1660, The Rand Corporation, Santa Monica, 1956) to present a framework for deriving a large class of cut-like inequalities for the hop-constrained path problem. A simple relation between the hop-constrained path polytope and the knapsack polytopes is also presented.