Sphere-separable partitions of multi-parameter elements

Boaz Golany, Frank K. Hwang, Uriel G. Rothblum

Research output: Contribution to journalArticlepeer-review

Abstract

We show the optimality of sphere-separable partitions for problems where n vectors in d-dimensional space are to be partitioned into p categories to minimize a cost function which is dependent in the sum of the vectors in each category; the sum of the squares of their Euclidean norms; and the number of elements in each category. We further show that the number of these partitions is polynomial in n. These results broaden the class of partition problems for which an optimal solution is guaranteed within a prescribed set whose size is polynomially bounded in n. Applications of the results are demonstrated through examples.

Original languageEnglish
Pages (from-to)838-845
Number of pages8
JournalDiscrete Applied Mathematics
Volume156
Issue number6
DOIs
StatePublished - 15 Mar 2008

Keywords

  • Combinatorial optimization
  • Partitions
  • Polynomial bounds
  • Separation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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