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Inverse eccentric vertex problem on networks

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  • Kien Nguyen
  • André Chassein

Abstract

This paper addresses the problem of optimally modifying the edge lengths such that a prespecified vertex becomes the furthest vertex from a given fixed vertex in the perturbed network. We call this problem the inverse eccentric vertex problem. We show that the problem is $$NP$$ N P -complete even on cactus graphs. However, if the underlying graph is a cycle or a tree, we develop efficient algorithms with linear time complexity. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Kien Nguyen & André Chassein, 2015. "Inverse eccentric vertex problem on networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 687-698, September.
    • Handle: RePEc:spr:cejnor:v:23:y:2015:i:3:p:687-698
    DOI: 10.1007/s10100-014-0367-2
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    References listed on IDEAS

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    1. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    2. 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.
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    Cited by:

    1. Tibor Csendes & Lidija Zadnik Stirn & Janez Žerovnik, 2015. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 523-525, September.
    2. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 773-790, September.
    3. Kien Trung Nguyen, 2016. "Inverse 1-Median Problem on Block Graphs with Variable Vertex Weights," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 944-957, March.

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