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Most Vital Segment Barriers

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Algorithms and Data Structures (WADS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11646))

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Abstract

We study continuous analogues of “vitality” for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of “most vital arcs” for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases.

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Notes

  1. 1.

    Other modeling choices could have been made; e.g, another way to avoid complete blockage could be to introduce a “protected zone” around s à la in works on geographic mincut [23]. Also a more generic view, outside our scope, could be to combine the flow and path problems into considering minimum-cost flows [9, 25] (the shortest path is the mincost flow of value 0) and explore how the barriers could influence both the capacity of the domain and the cost of the flow.

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Acknowledgements

M.L. and F.S. were partially supported by the Netherlands Organisation for Scientific Research (NWO) through project no 614.001.504 and 612.001.651, respectively.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, The Netherlands

    Irina Kostitsyna

  2. Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands

    Maarten Löffler & Frank Staals

  3. Communications and Transport Systems, ITN, Linköping University, Linköping, Sweden

    Valentin Polishchuk

Authors
  1. Irina Kostitsyna
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  2. Maarten Löffler
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  3. Valentin Polishchuk
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  4. Frank Staals
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Corresponding author

Correspondence to Frank Staals .

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Editors and Affiliations

  1. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Zachary Friggstad

  2. School of Computer Science, Carleton University, Manotick, ON, Canada

    Jörg-Rüdiger Sack

  3. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Mohammad R Salavatipour

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Kostitsyna, I., Löffler, M., Polishchuk, V., Staals, F. (2019). Most Vital Segment Barriers. In: Friggstad, Z., Sack, JR., Salavatipour, M. (eds) Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer Science(), vol 11646. Springer, Cham. https://doi.org/10.1007/978-3-030-24766-9_36

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  • DOI: https://doi.org/10.1007/978-3-030-24766-9_36

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  • Online ISBN: 978-3-030-24766-9

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