Amortized efficiency of list update and paging rules
Communications of the ACM
Online computation and competitive analysis
Online computation and competitive analysis
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
Online unit clustering: Variations on a theme
Theoretical Computer Science
An Improved Algorithm for Online Unit Clustering
Algorithmica
A Randomized Algorithm for Online Unit Clustering
Theory of Computing Systems
On the online unit clustering problem
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
| Hi-index | 5.23 |
Unit clustering is the problem of dividing a set of points from a metric space into a minimal number of subsets such that the points in each subset are enclosable by a unit ball. We continue the work, recently initiated by Chan and Zarrabi-Zadeh, on determining the competitive ratio of the online version of this problem. For the one-dimensional case, we develop a deterministic algorithm, improving the best known upper bound of 7/4 by Epstein and van Stee to 5/3. This narrows the gap to the best known lower bound of 8/5 to only 1/15. Our algorithm automatically leads to improvements in all higher dimensions as well. Finally, we strengthen the deterministic lower bound in two dimensions and higher from 2 to 13/6.