K-center and K-median problems in graded distances

Guo Hui Lin, Guoliang Xue

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Graded distances are generalizations of the Euclidean distance on points in R1. They have been used in the study of special cases of NP-hard problems. In this paper, we study the k-center and k-median problems with graded distance matrices. We first prove that the k-center problem is polynomial time solvable when the distance matrix is graded up the rows or graded down the rows. We then prove that the k-median problem is NP-complete when the distance matrix is graded up the rows or graded down the rows. An easy special case of the k-median problem with graded distance matrices is also discussed.

Original languageEnglish (US)
Pages (from-to)181-192
Number of pages12
JournalTheoretical Computer Science
Volume207
Issue number1
DOIs
StatePublished - Oct 28 1998
Externally publishedYes

Keywords

  • Computational complexity
  • Graded distance matrix
  • The k-center problem
  • The k-median problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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