Worst-case and Probabilistic Analysis of a Geometric Location Problem
Name
MIT-LCS-TM-153.pdf
Size
5.28 MB
Format
Adobe PDF
Checksum (MD5)
fd70cece1decec5c65a98a95e8501ab3
Author(s)
Papadimitriou, Christos H.
Date Issued
February 1980
Series/Report no.
MIT-LCS-TM-153
Abstract
We consider the problem of choosing K "medians" among n points on the Euclidean plane such that the sum of the distances from each of the n points to its closest median is minimized. We show that this problem is NP-complete. We also present two heuristics that produce arbitrarily good solutions with probability going to 1. One is a partition heuristic, and works when K grows lineraly -- or almost so -- with n. The other is the "honeycomb" heuristic, and is applicable to rates of grother of K of the form K ~ n^Є, 0<Є<1.
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