Solving the chromatic cone clustering problem via minimum spanning sphere

Authors:
Hu Ding;Jinhui Xu
Affiliations:
Department of Computer Science and Engineering, State University of New York at Buffalo;Department of Computer Science and Engineering, State University of New York at Buffalo
Venue:
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Year:
2011

Citing 7
Cited 0

On the complexity of some geometric problems in unbounded dimension

Journal of Symbolic Computation
The upper envelope of Voronoi surfaces and its applications

SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Approximate clustering via core-sets

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Smaller core-sets for balls

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs

SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Farthest-polygon Voronoi diagrams

ESA'07 Proceedings of the 15th annual European conference on Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study the following Chromatic Cone Clustering (CCC) problem: Given n point-sets with each containing k points in the first quadrant of the d-dimensional space Rd, find k cones apexed at the origin such that each cone contains at least one distinct point (i.e., different from other cones) from every point-set and the total size of the k cones is minimized, where the size of a cone is the angle from any boundary ray to its center line. CCC is motivated by an important biological problem and finds applications in several other areas. Our approaches for solving the CCC problem relies on solutions to the Minimum Spanning Sphere (MinSS) problem for point-sets. For the MinSS problem, we present two (1+ε)-approximation algorithms based on core-sets and ε-net respectively. With these algorithms, we then show that the CCC problem admits (1 + ε)-approximation solutions for constant k. Our results are the first solutions to these problems.