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On the number of separable partitions

Author

Listed:
  • Frank K. Hwang
  • Uriel G. Rothblum

    (Technion-Israel Institute of Technology)

Abstract

Consider partitions of a given set A of n distinct points in general position in ℝ d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.

Suggested Citation

  • Frank K. Hwang & Uriel G. Rothblum, 2011. "On the number of separable partitions," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 423-433, May.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:4:d:10.1007_s10878-009-9263-4
    DOI: 10.1007/s10878-009-9263-4
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    References listed on IDEAS

    as
    1. Chakravarty, Amiya K., 1982. "Inventory grouping for joint replenishment," Engineering Costs and Production Economics, Elsevier, vol. 7(1), pages 19-24, July.
    2. Shmuel Onn & Leonard J. Schulman, 2001. "The Vector Partition Problem for Convex Objective Functions," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 583-590, August.
    3. A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1982. "Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 30(5), pages 1018-1022, October.
    4. A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1985. "Consecutive Optimizers for a Partitioning Problem with Applications to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 33(4), pages 820-834, August.
    5. Shmuel Gal & Boris Klots, 1995. "Optimal Partitioning Which Maximizes the Sum of the Weighted Averages," Operations Research, INFORMS, vol. 43(3), pages 500-508, June.
    Full references (including those not matched with items on IDEAS)

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