TY - GEN
T1 - Solving the chromatic cone clustering problem via minimum spanning sphere
AU - Ding, Hu
AU - Xu, Jinhui
PY - 2011
Y1 - 2011
N2 - 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 R d , 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.
AB - 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 R d , 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.
KW - Chromatic
KW - Clustering
KW - Core-Set
KW - High Dimension
UR - https://www.scopus.com/pages/publications/79959966252
U2 - 10.1007/978-3-642-22006-7_65
DO - 10.1007/978-3-642-22006-7_65
M3 - Conference contribution
AN - SCOPUS:79959966252
SN - 9783642220050
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 773
EP - 784
BT - Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
T2 - 38th International Colloquium on Automata, Languages and Programming, ICALP 2011
Y2 - 4 July 2011 through 8 July 2011
ER -