Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Proceedings of the nineteenth annual symposium on Computational geometry
High-dimensional shape fitting in linear time
Proceedings of the nineteenth annual symposium on Computational geometry
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
| Hi-index | 0.00 |
Shape fitting is a fundamental optimization problem in computer science. In this paper, we present a general and unified technique for solving a certain family of such problems. Given a point set P in \mathbb{R}^d , this technique can be used to \varepsilon-approximate: (i) the min-width annulus and shell that contains P, (ii) minimum width cylindrical shell containing P, (iii) diameter, width, minimum volume bounding box of P, and (iv) all the previous measures for the case the points are moving. The running time of the resulting algorithms is 0(n + {1 \mathord{\left/ {\vphantom {1 {\varepsilon ^c }}} \right. \kern-\nulldelimiterspace} {\varepsilon ^c }}), where c is a constant that depends on the problem at hand.Our new general technique enables us to solve those problems without resorting to a careful and painful case by case analysis, as was previously done for those problems. Furthermore, for several of those problems our results are considerably simpler and faster than what was previously known. In particular, for the minimum width cylindrical shell problem, our solution is the first algorithm whose running time is subquadratic in n. (In fact we get running time linear in n.)