Approximation algorithms for min-sum p-clustering
Discrete Applied Mathematics
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A randomized approximation scheme for metric MAX-CUT
Journal of Computer and System Sciences
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Property testing and its connection to learning and approximation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation schemes for Metric Bisection and partitioning
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An LP rounding algorithm for approximating uncapacitated facility location problem with penalties
Information Processing Letters
Approximation algorithms for maximum dispersion
Operations Research Letters
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Traditionally, clustering problems are investigated under the assumption that all objects must be clustered. A shortcoming of this formulation is that a few distant objects, called outliers, may exert a disproportionately strong influence over the solution. In this work we investigate the k-min-sum clustering problem while addressing outliers in a meaningful way. Given a complete graph G = (V,E), a weight function w : E →IN0 on its edges, and $p \rightarrow {\it {IN}_{o}}$ a penalty function on its nodes, the penalized k-min-sum problem is the problem of finding a partition of V to k+1 sets, {S1,...,Sk+1}, minimizing $\sum_{i=1}^{k}$w(Si)+p(Sk+1), where for S⊆Vw(S) = $\sum_{e=\{{\it i},{\it j}\} \subset {\it S}}$we, and p(S) = $\sum_{i \in S}{^p_i}$. We offer an efficient 2-approximation to the penalized 1-min-sum problem using a primal-dual algorithm. We prove that the penalized 1-min-sum problem is NP-hard even if w is a metric and present a randomized approximation scheme for it. For the metric penalized k-min-sum problem we offer a 2-approximation.