Minimum-diameter covering problems

Esther M. Arkin*, Refael Hassin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).

Original languageEnglish
Pages (from-to)147-155
Number of pages9
Issue number3
StatePublished - Oct 2000


  • Approximation algorithms
  • Covering problems
  • Graph diameter
  • NP-complete


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