In this paper we present approximation algorithms for median problems in
metric spaces and xed-dimensional Euclidean space. Our algorithms use a new
method for transforming an optimal solution of the linear program relaxation
of the s-median problem into a provably good integral solution. This transfor-
mation technique is fundamentally di erent from the methods of randomized
and deterministic rounding [Rag, RaT] and the methods proposed in [LiV] in
the following way: Previous techniques never set variables with zero values in
the fractional solution to 1. This departure from previous methods is crucial
for the success of our algorithms.
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