Exact and Approximation Algorithms for Clustering

Exact and Approximation Algorithms for Clustering (Extended Abstract)

In this paper we present an n O(k 1?1=d) time algorithm for solving the k-center problem in R d , under L1 and L2 met-rics. The algorithm extends to other metrics, and to the discrete k-center problem. We also describe a simple (1+)-approximation algorithm for the k-center problem, with running time O(n log k) + (k==) O(k 1?1=d). Finally, we present a n O(k 1?1=d) time algorithm for solving the...

A Survey on Exact and Approximation Algorithms for Clustering

Given a set of point P in Rd, a clustering problem is to partition P into k subsets {P1, P2, · · · , Pk} in such a way that a given objective function is minimized. The most studied cost functions for a cluster, μ(Pi), are maximum or average radius of Pi, maximum diameter of Pi, and maximum width of Pi. The overall objective function is ⊕ μ(Pi), where ⊕ is typically the Lp-norm operator. The mo...

Approximation Algorithms for Clustering

Approximation Algorithms for Clustering Clustering items into groups is a fundamental problem in the information sciences. Many typical clustering optimization problems are NP-hard and so cannot be expected to be solved optimally in a reasonable amount of time. Although the use of heuristics is common, in this dissertation we seek approximation algorithms, whose performance ratio in relation to...

Exact and Approximation Algortihms for Clustering

In this paper we present a n O(k 1 1=d ) time algorithm for solving the k-center problem in R d , under L 1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete k-center problem, as well. We also describe a simple (1 + )-approximation algorithm for the k-center problem, with running time O(n log k) + (k= ) O(k 1 1=d ) . Finally, we present a n O(k 1 1=d...

Approximation Algorithms for Clustering Problems