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)
Fast stabbing of boxes in high dimensions
Theoretical Computer Science
Introduction to algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
A randomized algorithm for online unit clustering
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
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)
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We revisit the online unit clustering problem in one dimension which we recently introduced at WAOA'06: given a sequence of n points on the line, the objective is to partition the points into a minimum number of subsets, each enclosable by a unit interval. We present a new randomized online algorithm that achieves expected competitive ratio 11/6 against oblivious adversaries, improving the previous ratio of 15/8. This immediately leads to improved upper bounds for the problem in two and higher dimensions as well.