BIB-VERSION:: CS-TR-v2.0
ID:: ncstrl.dartmouthcs//TR99-344
ENTRY:: March 26, 1999
ORGANIZATION:: Dartmouth College, Computer Science
TITLE:: Greedy Approximation Algorithms for K-Medians by Randomized Rounding
TYPE:: Technical Report (paper)
REVISION:: 1
AUTHOR:: Young, Neal E.
DATE:: March 1999
RETRIEVAL:: For a paper copy, email <reports@cs.dartmouth.edu>
RETRIEVAL:: For a paper copy, write to
       Technical Report Librarian
       Department of Computer Science
       Dartmouth College
       6211 Sudikoff Laboratory
       Hanover, NH 03755-3510
       USA
RETRIEVAL:: Compressed Postscript at http://www.cs.dartmouth.edu/reports/TR99-344.ps.Z
RETRIEVAL:: PDF at http://www.cs.dartmouth.edu/reports/TR99-344.pdf
ABSTRACT:: 
  We give an improved approximation algorithm for the general k-medians
problem.  Given any \epsilon>0, the algorithm finds a solution of total
distance at most D(1+\epsilon) using at most k ln(n+n/\epsilon) medians
(a.k.a. sites), provided some solution of total distance D using k medians
exists.  This improves over the best previous bound (w.r.t. the number of
medians) by a factor of \Omega(1/\epsilon) provided 1/\epsilon=n^O(1).  The
algorithm is a greedy algorithm, derived using the method of oblivious
randomized rounding.  It requires at most k ln(n+n/\epsilon) linear-time
iterations.  We also derive algorithms for fractional and weighted variants
of the problem.
END:: ncstrl.dartmouthcs//TR99-344