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Optimal Partitioning Which Maximizes the Sum of the Weighted Averages

Author

Listed:
  • Shmuel Gal

    (IBM Israel Science and Technology Ltd., Haifa, Israel)

  • Boris Klots

    (IBM Israel Science and Technology Ltd., Haifa, Israel)

Abstract

We consider an optimal partitioning problem that occurs in the assignment of computer jobs to a multiple cache and in other combinatorial optimization problems: For a given set of n elements, where each element i has a given frequency p i and a specific weight w i , we would like to divide the elements into m mutually exclusive groups such that the sum over all the groups of the average group weight is maximal. We characterize the optimal solution and present an algorithm which is polynomial in n for obtaining the optimal partitioning. Optimal partitioning policies for two groups has an especially simple characterization: There exist two numbers α and β, with min w i w i , such that all the elements with weight w i satisfying α ≤ w i ≤ β belong to one group and all other elements belong to the other group. A modification of this policy gives the optimal partitioning for an arbitrary number of groups.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:3:p:500-508
    DOI: 10.1287/opre.43.3.500
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    Citations

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    Cited by:

    1. Arbib, Claudio & Rossi, Fabrizio, 2000. "An optimization problem arising in the design of multiring systems," European Journal of Operational Research, Elsevier, vol. 124(1), pages 63-76, July.
    2. Huilan Chang & Frank K. Hwang & Uriel G. Rothblum, 2012. "A new approach to solve open-partition problems," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 61-78, January.
    3. Chung‐Lun Li & Zhi‐Long Chen, 2006. "Bin‐packing problem with concave costs of bin utilization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 298-308, June.
    4. Gerard J. Chang & Fu-Loong Chen & Lingling Huang & Frank K. Hwang & Su-Tzu Nuan & Uriel G. Rothblum & I-Fan Sun & Jan-Wen Wang & Hong-Gwa Yeh, 1998. "Sortabilities of Partition Properties," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 413-427, December.
    5. 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.

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