Efficient approximation algorithms for clustering point-sets

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

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...

Approximation Algorithms for Clustering Problems

Approximation Algorithms for Co-Clustering

Approximation Algorithms for Clique Clustering

A clique clustering of a graph is a partitioning of its vertices into disjoint cliques. The quality of a clique clustering is measured by the total number of edges in its cliques. We consider the online variant of the clique clustering problem, where the vertices of the input graph arrive one at a time. At each step, the newly arrived vertex forms a singleton clique, and the algorithm can merge...