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STOC
1998
ACM
139views Algorithms» more  STOC 1998»
10 years 8 months ago
Approximation Schemes for Euclidean k-Medians and Related Problems
In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances fro...
Sanjeev Arora, Prabhakar Raghavan, Satish Rao
JCSS
2002
199views more  JCSS 2002»
10 years 3 months ago
A Constant-Factor Approximation Algorithm for the k-Median Problem
We present the first constant-factor approximation algorithm for the metric k-median problem. The k-median problem is one of the most well-studied clustering problems, i.e., those...
Moses Charikar, Sudipto Guha, Éva Tardos, D...
FOCS
2010
IEEE
10 years 2 months ago
Stability Yields a PTAS for k-Median and k-Means Clustering
We consider k-median clustering in finite metric spaces and k-means clustering in Euclidean spaces, in the setting where k is part of the input (not a constant). For the k-means pr...
Pranjal Awasthi, Avrim Blum, Or Sheffet
FOCS
2008
IEEE
10 years 10 months ago
A Polynomial-Time Approximation Scheme for Euclidean Steiner Forest
We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed ǫ > 0 and given n terminals in the plane ...
Glencora Borradaile, Philip N. Klein, Claire Mathi...
SODA
2010
ACM
172views Algorithms» more  SODA 2010»
11 years 1 months ago
A quasi-polynomial time approximation scheme for Euclidean capacitated vehicle routing
In the capacitated vehicle routing problem, introduced by Dantzig and Ramser in 1959, we are given the locations of n customers and a depot, along with a vehicle of capacity k, an...
Aparna Das, Claire Mathieu
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