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Partitioning a weighted partial order

Author

Listed:
  • Linda S. Moonen

    (Katholieke Universiteit Leuven)

  • Frits C. R. Spieksma

    (Katholieke Universiteit Leuven)

Abstract

The problem of partitioning a partially ordered set into a minimum number of chains is a well-known problem. In this paper we study a generalization of this problem, where we not only assume that the chains have bounded size, but also that a weight w i is given for each element i in the partial order such that w i ≤w j if i ≺ j. The problem is then to partition the partial order into a minimum-weight set of chains of bounded size, where the weight of a chain equals the weight of the heaviest element in the chain. We prove that this problem is $\mathcal{APX}$ -hard, and we propose and analyze lower bounds for this problem. Based on these lower bounds, we exhibit a 2-approximation algorithm, and show that it is tight. We report computational results for a number of real-world and randomly generated problem instances.

Suggested Citation

  • Linda S. Moonen & Frits C. R. Spieksma, 2008. "Partitioning a weighted partial order," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 342-356, May.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:4:d:10.1007_s10878-007-9086-0
    DOI: 10.1007/s10878-007-9086-0
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    References listed on IDEAS

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    1. Linda S. Moonen & Frits C. R. Spieksma, 2006. "Exact Algorithms for a Loading Problem with Bounded Clique Width," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 455-465, November.
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