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Fast approximation algorithms for routing problems with hop-wise constraints

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  • Amir Elalouf

Abstract

Given a graph G(N,A) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subject to an end-to-end delay constraint. The problem (with a single constraint) is NP-hard, and has been studied by many researchers who found fully polynomial approximation schemes (FPAS) for this problem. The current paper focuses on a generalized CRP version, CRP with hop-wise constraints (CRPH). In the generalized version, instead of one constraint there are up to n−1 special-type constraints, where n is the number of nodes. An FPAS based on interval partitioning is proposed for both the minimization and the maximization versions of CRPH. For G(N,A) with n nodes and m arcs, the complexity of the algorithm is O(mn 2 /ε). Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Amir Elalouf, 2014. "Fast approximation algorithms for routing problems with hop-wise constraints," Annals of Operations Research, Springer, vol. 222(1), pages 279-291, November.
    • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:279-291:10.1007/s10479-013-1308-5
    DOI: 10.1007/s10479-013-1308-5
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    1. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    2. Christian Artigues & Dominique Feillet, 2008. "A branch and bound method for the job-shop problem with sequence-dependent setup times," Annals of Operations Research, Springer, vol. 159(1), pages 135-159, March.
    3. Henig, Mordechai I., 1986. "The shortest path problem with two objective functions," European Journal of Operational Research, Elsevier, vol. 25(2), pages 281-291, May.
    4. P. Eveborn & M. Rönnqvist, 2004. "Scheduler – A System for Staff Planning," Annals of Operations Research, Springer, vol. 128(1), pages 21-45, April.
    5. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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