Packing Interdiction and Partial Covering Problems

  • Michael Dinitz
  • Anupam Gupta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7801)


In the Packing Interdiction problem we are given a packing LP together with a separate interdiction cost for each LP variable and a global interdiction budget. Our goal is to harm the LP: which variables should we forbid the LP from using (subject to forbidding variables of total interdiction cost at most the budget) in order to minimize the value of the resulting LP? Interdiction problems on graphs (interdicting the maximum flow, the shortest path, the minimum spanning tree, etc.) have been considered before; here we initiate a study of interdicting packing linear programs. Zenklusen showed that matching interdiction, a special case, is NP-hard and gave a 4-approximation for unit edge weights. We obtain an constant-factor approximation to the matching interdiction problem without the unit weight assumption. This is a corollary of our main result, an O(logq · min {q, logk})-approximation to Packing Interdiction where q is the row-sparsity of the packing LP and k is the column-sparsity.


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  1. 1.
    Phillips, C.A.: The network inhibition problem. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, STOC 1993, pp. 776–785 (1993)Google Scholar
  2. 2.
    Burch, C., Carr, R., Krumke, S., Marathe, M., Phillips, C., Sundberg, E.: A decomposition-based pseudoapproximation algorithm for network flow inhibition. In: Network Interdiction and Stochastic Integer Programming, pp. 51–68 (2003)Google Scholar
  3. 3.
    Wood, R.: Deterministic network interdiction. Mathematical and Computer Modelling 17, 1–18 (1993)MATHCrossRefGoogle Scholar
  4. 4.
    Zenklusen, R.: Network flow interdiction on planar graphs. Discrete Appl. Math. 158, 1441–1455 (2010)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Fulkerson, D.R., Harding, G.C.: Maximizing Minimum Source-Sink Path Subject To A Budget Constraint. Mathematical Programming 13, 116–118 (1977)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Israeli, E., Wood, R.K.: Shortest-path network interdiction. Networks 40, 2002 (2002)Google Scholar
  7. 7.
    Frederickson, G.N., Solis-Oba, R.: Increasing the weight of minimum spanning trees. In: SODA 1996, pp. 539–546 (1996)Google Scholar
  8. 8.
    Zenklusen, R.: Matching interdiction. Discrete Appl. Math. 158, 1676–1690 (2010)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Zenklusen, R., Ries, B., Picouleau, C., de Werra, D., Costa, M.C., Bentz, C.: Blockers and transversals. Discrete Mathematics 309, 4306–4314 (2009)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Kasiviswanathan, S.P., Pan, F.: Matrix Interdiction Problem. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 219–231. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Könemann, J., Parekh, O., Segev, D.: A unified approach to approximating partial covering problems. Algorithmica 59, 489–509 (2011)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Kearns, M.J.: The computational complexity of machine learning. PhD thesis, Harvard University, Cambridge, MA, USA (1990)Google Scholar
  13. 13.
    Slavík, P.: Improved performance of the greedy algorithm for partial cover. Inf. Process. Lett. 64, 251–254 (1997)CrossRefGoogle Scholar
  14. 14.
    Bar-Yehuda, R.: Using homogeneous weights for approximating the partial cover problem. J. Algorithms 39, 137–144 (2001)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Fujito, T.: On approximation of the submodular set cover problem. Oper. Res. Lett. 25, 169–174 (1999)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Bar-Yehuda, R., Even, S.: A linear-time approximation algorithm for the weighted vertex cover problem. Journal of Algorithms 2, 198–203 (1981)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael Dinitz
    • 1
  • Anupam Gupta
    • 2
  1. 1.Weizmann Institute of ScienceIsrael
  2. 2.Carnegie Mellon UniversityUSA

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