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Robustly Assigning Unstable Items

  • Ananya Christman
  • Christine Chung
  • Nicholas Jaczko
  • Scott Westvold
  • David S. Yuen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

We study the Robust Assignment Problem where the goal is to assign items of various types to containers without exceeding container capacity. We seek an assignment that uses the fewest number of containers and is robust, that is, if any item of type \(t_i\) becomes corrupt causing the containers with type \(t_i\) to become unstable, every other item type \(t_j \ne t_i\) is still assigned to a stable container. We begin by presenting an optimal polynomial-time algorithm that finds a robust assignment using the minimum number of containers for the case when the containers have infinite capacity. Then we consider the case where all containers have some fixed capacity and give an optimal polynomial-time algorithm for the special case where each type of item has the same size. When the sizes of the item types are nonuniform, we provide a polynomial-time 2-approximation for the problem. We also prove that the approximation ratio of our algorithm is no lower than 1.813. We conclude with an experimental evaluation of our algorithm.

References

  1. 1.
    Chekuri, C., Khanna, S.: A PTAS for the multiple knapsack problem. In: Symposium on Discrete Algorithms (SODA) (2000)Google Scholar
  2. 2.
    Epstein, L., Levin, A.: On bin packing with conflicts. In: Erlebach, T., Kaklamanis, C. (eds.) WAOA 2006. LNCS, vol. 4368, pp. 160–173. Springer, Heidelberg (2007).  https://doi.org/10.1007/11970125_13CrossRefGoogle Scholar
  3. 3.
    Fleischer, L., Goemans, M.X., Mirrokni, V.S., Sviridenko, M.: Tight approximation algorithms for maximum general assignment problems. In: Proceedings of the Symposium on Discrete Algorithms (2006)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  5. 5.
    Jansen, K.: An approximation scheme for bin packing with conflicts. J. Comb. Optim. 3(4), 363–377 (1999)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jansen, K., Öhring, S.: Approximation algorithms for time constrained scheduling. Inf. Comput. 132(2), 85–108 (1997)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Korupolu, M., Rajaraman, R.: Robust and probabilistic failure-aware placement. In: Proceedings of the Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 213–224 (2016)Google Scholar
  8. 8.
    Korupolu, M., Meyerson, A., Rajaraman, R., Tagiku, B.: Robust and probabilistic failure-aware placement. Math. Program. 154(1–2), 493–514 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mills, K., Chandrasekaran, R., Mittal, N.: Algorithms for optimal replica placement under correlated failure in hierarchical failure domains. Theor. Comput. Sci. (2017, pre-print)Google Scholar
  10. 10.
    Rahman, R., Barker, K., Alhajj, R.: Replica placement strategies in data grid. J. Grid Comput. 6(1), 103–123 (2008)CrossRefGoogle Scholar
  11. 11.
    Shmoys, D., Tardos, E.: An approximation algorithm for the generalized assignment problem. Math. Program. 62(3), 461–474 (1993)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sperner, E.: Ein Satz über Untermengen einer endlichen Menge. Mathematische Zeitschrift 27(1), 544–548 (1928)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Stein, C., Zhong, M.: Scheduling when you don’t know the number of machines. In: Proceedings of the Symposium on Discrete Algorithms (SODA) (2018)CrossRefGoogle Scholar
  14. 14.
    Stirling, J.: Methodus differentialis, sive tractatus de summation et interpolation serierum infinitarium, London (1730)Google Scholar
  15. 15.
    Urgaonkar, B., Rosenberg, A., Shenoy, P.: Application placement on a cluster of servers. Int. J. Found. Comput. Sci. 18(5), 1023–1041 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceMiddlebury CollegeMiddleburyUSA
  2. 2.Department of Computer ScienceConnecticut CollegeNew LondonUSA
  3. 3.Department of MathematicsUniversity of HawaiiHonoluluUSA

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