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Approximation Algorithms for Certain Network Improvement Problems

Author

Listed:
  • Sven O. Krumke

    (Konrad-Zuse-Zentrum für Informationstechnik Berlin)

  • Madhav V. Marathe

    (Madhav V. Marathe, Los Alamos National Laboratory)

  • Hartmut Noltemeier

    (University of Würzburg)

  • R. Ravi

    (Carnegie Mellon University)

  • S. S. Ravi

    (University at Albany–SUNY)

Abstract

We study budget constrained network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V, E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that specifies the cost of upgrading the edge by an amount t. A reduction strategy specifies for each edge e the amount by which the length ℓ(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to find an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the models and definitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.

Suggested Citation

  • Sven O. Krumke & Madhav V. Marathe & Hartmut Noltemeier & R. Ravi & S. S. Ravi, 1998. "Approximation Algorithms for Certain Network Improvement Problems," Journal of Combinatorial Optimization, Springer, vol. 2(3), pages 257-288, September.
    • Handle: RePEc:spr:jcomop:v:2:y:1998:i:3:d:10.1023_a:1009798010579
    DOI: 10.1023/A:1009798010579
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi, 2020. "Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks," Annals of Operations Research, Springer, vol. 289(2), pages 153-172, June.
    2. Burkard, Rainer E. & Lin, Yixun & Zhang, Jianzhong, 2004. "Weight reduction problems with certain bottleneck objectives," European Journal of Operational Research, Elsevier, vol. 153(1), pages 191-199, February.
    3. Maya Duque, Pablo A. & Coene, Sofie & Goos, Peter & Sörensen, Kenneth & Spieksma, Frits, 2013. "The accessibility arc upgrading problem," European Journal of Operational Research, Elsevier, vol. 224(3), pages 458-465.
    4. Guan, Xiucui & Zhang, Jianzhong, 2007. "Improving multicut in directed trees by upgrading nodes," European Journal of Operational Research, Elsevier, vol. 183(3), pages 971-980, December.
    5. Guan, Xiucui & Zhang, Jianzhong, 2006. "A class of node based bottleneck improvement problems," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1540-1552, November.
    6. Michael Holzhauser & Sven O. Krumke & Clemens Thielen, 2016. "Budget-constrained minimum cost flows," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1720-1745, May.
    7. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    8. Elisabeth Gassner, 2009. "A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric," Annals of Operations Research, Springer, vol. 172(1), pages 393-404, November.
    9. Gassner, Elisabeth, 2009. "Up- and downgrading the 1-center in a network," European Journal of Operational Research, Elsevier, vol. 198(2), pages 370-377, October.

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