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Robustly assigning unstable items

Author

Listed:
  • Ananya Christman

    (Middlebury College)

  • Christine Chung

    (Connecticut College)

  • Nicholas Jaczko

    (Middlebury College)

  • Scott Westvold

    (Middlebury College)

  • David S. Yuen

    (University of Hawaii)

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 $$t_i$$ t i becomes corrupt causing the containers with type $$t_i$$ t i to become unstable, every other item type $$t_j \ne t_i$$ t j ≠ 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.

Suggested Citation

  • Ananya Christman & Christine Chung & Nicholas Jaczko & Scott Westvold & David S. Yuen, 2022. "Robustly assigning unstable items," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1556-1577, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-019-00515-w
    DOI: 10.1007/s10878-019-00515-w
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    References listed on IDEAS

    as
    1. Klaus Jansen, 1999. "An Approximation Scheme for Bin Packing with Conflicts," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 363-377, December.
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