Minimum-diameter covering problems

نویسندگان

  • Esther M. Arkin
  • Refael Hassin
چکیده

A set V and a collection of (possibly non-disjoint) 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 deened as the maximum distance of 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 6 = NP).

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عنوان ژورنال:
  • Networks

دوره 36  شماره 

صفحات  -

تاریخ انتشار 2000