Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chan, T.M., Zarrabi-Zadeh, H.: A randomized algorithm for online unit clustering. In: Erlebach, T., Kaklamanis, C. (eds.) WAOA 2006. LNCS, vol. 4368, pp. 121–131. Springer, Heidelberg (2007)
Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. SIAM J. Comput. 33(6), 1417–1440 (2004)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Fotakis, D.: Incremental algorithms for facility location and k-median. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 347–358. Springer, Heidelberg (2004)
Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are NP-complete. Inform. Process. Lett. 12(3), 133–137 (1981)
Gonzalez, T.: Covering a set of points in multidimensional space. Inform. Process. Lett. 40, 181–188 (1991)
Gyárfás, A., Lehel, J.: On-line and First-Fit colorings of graphs. J. Graph Theory 12, 217–227 (1988)
Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32, 130–136 (1985)
Kierstead, H.A., Qin, J.: Coloring interval graphs with First-Fit. SIAM J. Discrete Math. 8, 47–57 (1995)
Meyerson, A.: Online facility location. In: Proc. 42nd IEEE Sympos. Found. Comput. Sci., pp. 426–433 (2001)
Nielsen, F.: Fast stabbing of boxes in high dimensions. Theoret. Comput. Sci. 246, 53–72 (2000)
Tanimoto, S.L., Fowler, R.J.: Covering image subsets with patches. In: Proc. 5th International Conf. on Pattern Recognition, pp. 835–839 (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zarrabi-Zadeh, H., Chan, T.M. (2007). An Improved Algorithm for Online Unit Clustering. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-73545-8_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73544-1
Online ISBN: 978-3-540-73545-8
eBook Packages: Computer ScienceComputer Science (R0)