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Inverse Problems of Matroid Intersection

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  • Cai Mao-Cheng

    (Academia Sinica)

Abstract

In this paper we study the inverse problem of matroid intersection: Two matroids M 1 = (E, $${\mathcal{I}}$$ 1) and M 2 = (E, $${\mathcal{I}}$$ 2), their intersection B, and a weight function w on E are given. We try to modify weight w, optimally and with bounds, such that B becomes a maximum weight intersection under the modified weight. It is shown in this paper that the problem can be formulated as a combinatorial linear program and can be further transformed into a minimum cost circulation problem. Hence it can be solved by strongly polynomial time algorithms. We also give a necessary and sufficient condition for the feasibility of the problem. Finally we extend the discussion to the version of the problem with Multiple Intersections.

Suggested Citation

  • Cai Mao-Cheng, 1999. "Inverse Problems of Matroid Intersection," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 465-474, December.
    • Handle: RePEc:spr:jcomop:v:3:y:1999:i:4:d:10.1023_a:1009883605691
    DOI: 10.1023/A:1009883605691
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    References listed on IDEAS

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    1. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
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