An Improved Algorithm for Online Unit Clustering
- 84 Downloads
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.
KeywordsOnline algorithms Randomized algorithms Unit clustering
Unable to display preview. Download preview PDF.
- 1.Chan, T.M., Zarrabi-Zadeh, H.: A randomized algorithm for online unit clustering. In: Proceedings of the 4th Workshop on Approximation and Online Algorithms. Lecture Notes in Computer Science, vol. 4368, pp. 121–131. Springer, Berlin (2006). To appear in Theory of Computing Systems CrossRefGoogle Scholar
- 5.Fotakis, D.: Incremental algorithms for facility location and k-median. In: Proceedings of the 12th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 3221, pp. 347–358. Springer, Berlin (2004) Google Scholar
- 11.Meyerson, A.: Online facility location. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, pp. 426–433 (2001) Google Scholar
- 13.Tanimoto, S.L., Fowler, R.J.: Covering image subsets with patches. In: Proceedings of the 5th International Conference on Pattern Recognition, pp. 835–839 (1980) Google Scholar