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Optimal Partitions

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Abstract

This chapter provides a survey on the problem of partitioning points in the d-dimensional space with the goal of maximizing a given objective function; the survey is based on the forthcoming book (Hwang FK, Rothblum UG (2011b) Partitions: optimality and clustering. World Scientific). The first two sections describe the framework, terminology, and some background material that are useful for the analysis of the partition problem. The middle two sections study the case of d = 1, and the last two sections study the case of general d. Results are presented without proofs, but with motivations, comments, and references. Complete proofs can also be found in the forthcoming book.

Work of Uriel G. Rothblum was supported by The Israel Science Foundation (Grant 669/06).

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Author information

Authors and Affiliations

  1. National Chiao Tung University (Retired), Hsinchu, People’s Republic of China

    Frank K. Hwang

  2. Faculty of Industrial Engineering and Management Science, Technion - Israel Institute of Technology, Bloomfield – 511, 32000, Haifa, Israel

    Uriel G. Rothblum

Authors
  1. Frank K. Hwang
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  2. Uriel G. Rothblum
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Corresponding authors

Correspondence to Frank K. Hwang or Uriel G. Rothblum .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Hwang, F.K., Rothblum, U.G. (2013). Optimal Partitions. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_40

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