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Algorithms and time complexity of the request-service problem

Author

Listed:
  • Chunmei Liu

    (Howard University)

  • Legand Burge

    (Howard University)

  • Ajoni Blake

    (Howard University)

Abstract

Given a number of users each of which provides a set of services with a cost for each service and has a set of requests to be satisfied, the goal of the request-service problem is to find a feasible solution that satisfies all requests of each user with minimum cost. In addition, a feasible solution must satisfy an additional constraint. Specifically, if user A provides a service to user B, B should provide a service back to A either directly or indirectly through other users. In this paper, we studied the complexity of this problem. We show that there exists a polynomial time algorithm that can compute a feasible solution with minimum cost if such a solution exists. However, if a feasible solution does not exist, the problem of maximizing the number of satisfied users (i.e., all requests of the users are satisfied) is NP-hard.

Suggested Citation

  • Chunmei Liu & Legand Burge & Ajoni Blake, 2010. "Algorithms and time complexity of the request-service problem," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 180-193, August.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:2:d:10.1007_s10878-008-9202-9
    DOI: 10.1007/s10878-008-9202-9
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    References listed on IDEAS

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    1. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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    More about this item

    Keywords

    Request-service; Disjoint cycle cover; MAX2SAT;
    All these keywords.

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