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. T
he 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 thes
e basic problems, and we prove in other cases that no such algorithms exist
(assuming P not equal NP). (C) 2000 John Wiley & Sons, Inc.