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Journal of Global Optimization

, Volume 18, Issue 3, pp 275–282 | Cite as

Supermodularity in Various Partition Problems

  • F. K. Hwang
  • M. M. Liao
  • Chiuyuan Chen
Article

Abstract

Supermodular and submodular functions have attracted a great deal of attention since the seminal paper of Lovász. Recently, supermodular functions were studied in the context of some optimal partition problems. We completely answer a question arisen there whether a certain partition function is supermodular.

Partition Supermodularity Sum-partition 

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References

  1. 1.
    Gao, B., Hwang, F.K., Li, W.W.-C. and Rothblum, U.G. (1999), Partition polytopes over 1-dimensional points, Math. Prog. 85: 335-362.Google Scholar
  2. 2.
    Hwang, F.K. and Rothblum, U.G., Partitions: Clustering and Optimality, (in progress).Google Scholar
  3. 3.
    Lovász, L., Submodular functions and complexity, in A. Bachem et al. (eds.), Mathematical Programming: The State of the Art, pp. 235-257.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • F. K. Hwang
    • 1
  • M. M. Liao
    • 1
  • Chiuyuan Chen
    • 1
  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan, R.O.C

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