Journal ArticleDOI
Single Facility $l_p $-Distance Minimax Location
Zvi Drezner,George O. Wesolowsky +1 more
TLDR
In this article, the authors discuss the problem of locating a new facility among n given demand points on a plane, where the maximum weighted distance to demand points must be minimized and the general $l_p $-norm $( p\geqq 1)$ is used as distance measure.Abstract:
We discuss the problem of locating a new facility among n given demand points on a plane. The maximum weighted distance to demand points must be minimized. The general $l_p $-norm $( p\geqq 1)$ is used as distance measure. The method is quite fast computationally: for example, a 3000 demand point problem in $l_p $ is solved in half a second.read more
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Proceedings ArticleDOI
Linear-time algorithms for linear programming in R3 and related problems
TL;DR: A linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane, which disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time.
Journal ArticleDOI
Heuristic solution methods for two location problems with unreliable facilities
TL;DR: The p-median and p-centre problems are generalized by considering the possibility that one or more of the facilities may become inactive, and an heuristic procedure is presented for each problem.
Journal ArticleDOI
The Planar Two-Center and Two-Median Problems
TL;DR: Algorithms for the solution of planar location-allocation problems with two new facilities are presented, addressing both the minimax or “two-center”, and minisum or ”two-median” problems.
Journal ArticleDOI
Efficient Algorithms for the Weighted Minimum Circle Problem
Donald W. Hearn,James Vijay +1 more
TL;DR: A classification scheme, based on fundamental mathematical programming concepts, for algorithms which solve both weighted and unweighted versions of the weighted minimum covering circle problem is introduced.