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SWAT
2010
Springer

Better Bounds on Online Unit Clustering

9 years 7 months ago
Better Bounds on Online Unit Clustering
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.
Martin R. Ehmsen, Kim S. Larsen
Added 11 Jul 2010
Updated 11 Jul 2010
Type Conference
Year 2010
Where SWAT
Authors Martin R. Ehmsen, Kim S. Larsen
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