Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Coloring interval graphs with First-Fit
Discrete Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Better streaming algorithms for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
Online interval coloring and variants
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Variable-Size Rectangle Covering
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
On the online unit clustering problem
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
On the online unit clustering problem
ACM Transactions on Algorithms (TALG)
An improved algorithm for online unit clustering
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Hi-index | 0.00 |
In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naïve upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.