Vertex Downgrading to Minimize Connectivity

Authors Hassene Aissi, Da Qi Chen, R. Ravi



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Author Details

Hassene Aissi
  • Paris Dauphine University, France
Da Qi Chen
  • Carnegie Mellon University, Pittsburgh, PA, USA
R. Ravi
  • Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA

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Hassene Aissi, Da Qi Chen, and R. Ravi. Vertex Downgrading to Minimize Connectivity. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.SWAT.2020.5

Abstract

We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria (4,4)-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. We accomplish this with an LP relaxation and rounding using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of k levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get a (4k,4k)-approximation for this case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Vertex Interdiction
  • Vertex Downgrading
  • Network Interdiction
  • Approximation Algorithm

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References

  1. Hassene Aissi, Da Qi Chen, and R. Ravi. Downgrading to minimize connectivity, 2019. URL: http://arxiv.org/abs/1911.11229.
  2. C. Burch, R. Carr, S. Krumke, M. Marathe, C. Phillips, and E. Sundberg. A decomposition-based pseudoapproximation algorithm for network flow inhibition. In Woodruff D. L., editor, Network Interdiction and Stochastic Integer Programming, volume 26, pages 51-68. springer, 2003. Google Scholar
  3. Stephen R Chestnut and Rico Zenklusen. Interdicting structured combinatorial optimization problems with 0, 1-objectives. Mathematics of Operations Research, 42(1):144-166, 2016. Google Scholar
  4. Stephen R Chestnut and Rico Zenklusen. Hardness and approximation for network flow interdiction. Networks, 69(4):378-387, 2017. Google Scholar
  5. Julia Chuzhoy, Yury Makarychev, Aravindan Vijayaraghavan, and Yuan Zhou. Approximation algorithms and hardness of the k-route cut problem. ACM Transactions on Algorithms (TALG), 12(1):2, 2016. Google Scholar
  6. Julia Chuzoy. Flows, cuts and integral routing in graphs - an approximation algorithmist’s perspective. In Proc. of the International Congress of Mathematicians, pages 585-607, 2014. Google Scholar
  7. Bruce Golden. A problem in network interdiction. Naval Research Logistics Quarterly, 25(4):711-713, 1978. Google Scholar
  8. Bertrand Guenin, Jochen Könemann, and Levent Tuncel. A gentle introduction to optimization. Cambridge University Press, 2014. Google Scholar
  9. Guru Guruganesh, Laura Sanita, and Chaitanya Swamy. Improved region-growing and combinatorial algorithms for k-route cut problems. In Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, pages 676-695. Society for Industrial and Applied Mathematics, 2015. Google Scholar
  10. T. E. Harris and F. S. Ross. Fundamentals of a method for evaluating rail net capacities. Technical report, RAND CORP SANTA MONICA CA, Santa Monica, California, 1955. Google Scholar
  11. Eitan Israeli and R Kevin Wood. Shortest-path network interdiction. Networks: An International Journal, 40(2):97-111, 2002. Google Scholar
  12. André Linhares and Chaitanya Swamy. Improved algorithms for mst and metric-tsp interdiction. Proceedings of 44th International Colloquium on Automata, Languages, and Programming, 32:1-14, 2017. Google Scholar
  13. Christos H Papadimitriou and Mihalis Yannakakis. On the approximability of trade-offs and optimal access of web sources. In Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 86-92. IEEE, 2000. Google Scholar
  14. Cynthia A. Phillips. The network inhibition problem. In Proceedings of the Twenty-fifth Annual ACM Symposium on Theory of Computing, STOC '93, pages 776-785, New York, NY, USA, 1993. ACM. URL: https://doi.org/10.1145/167088.167286.
  15. Alexander Schrijver. On the history of the transportation and maximum flow problems. Mathematical Programming, 91(3):437-445, 2002. Google Scholar
  16. R. Wood. Deterministic network interdiction. Mathematical and Computer Modeling, 17(2):1-18, 1993. Google Scholar
  17. R. Zenklusen. Matching interdiction. Discrete Applied Mathematics, 145(15), 2010. Google Scholar
  18. R. Zenklusen. Network flow interdiction on planar graphs. Discrete Applied Mathematics, 158(13), 2010. Google Scholar
  19. R. Zenklusen. Connectivity interdiction. Operations Research Letters, 42(67):450-454, 2014. Google Scholar
  20. R. Zenklusen. An 𝒪(1) approximation for minimum spanning tree interdiction. Proceedings of 56th Annual IEEE Symposium on Foundations of Computer Science, pages 709-728, 2015. Google Scholar
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