New Algorithms for k-Center and Extensions
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems
Computational Optimization and Applications
| Hi-index | 0.00 |
This thesis deals with problems at the intersection of computational geometry, optimization, graphics, and machine learning. Geometric clustering is one such problem we explore. We develop fast approximation algorithms for clustering problems like the k-center problem and minimum enclosing ellipsoid problem based on the idea of core sets. We also explore an application of the 1-center problem to recognition of people based on their hand outlines. Another problem we consider in this thesis is how to reconstruct curves and surfaces from given sample points. We show implementations of algorithms that can handle noise for reconstructing curves in two dimensions. Based on Delaunay triangulations, we develop a surface reconstructor for a given set of sample points in three dimensions. When dealing with massive data sets, it is important to consider the effect of memory hierarchies on algorithms. We explore this problem in our research on cache oblivious algorithms. We develop a practical cache oblivious algorithm to compute Delaunay triangulations of large point sets. We end the thesis with another optimization problem of approximately finding large empty convex bodies inside closed objects under various assumptions.