Abstract
An optimal algorithm is presented about Conflict-Free Coloring for connected subgraphs of chain of rings. Suppose the length of the chain is |C| and the maximum length of rings is |R|. A presented algorithm in [1] for a Chain of rings used O(log|C|.log|R|) colors but this algorithm uses O(log|C|+log|R|) colors. The coloring earned by this algorithm has the unique-min property, that is, the unique color is also minimum.
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.
Similar content being viewed by others
References
Georgia, K., Aris, P., Katerina, P.: Conflict-free Coloring for Connected Subgraphs of Trees and Trees of Rings. In: Proc. 11th Panhellenic Conference in Informatics (2007)
Even, G., Lotker, Z., Ron, D., Smorodinsky, S.: Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks. SIAM Journal on Computing 33, 94–136; Also in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS) (2002)
Bar-Noy, A., Cheilaris, P., Lampis, M., Zachos, S.: Conflict-free coloring graphs and other related problems (2006) (manuscript)
Cheilaris, P., Specker, E., Zachos, S.: Neochromatica (2006) (manuscript)
Bar-Noy, A., Cheilaris, P., Smorodinsky, S.: Conflict-free coloring for intervals: from offline to online. In: Proceedings of the 18th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 2006), Cambridge, Massachusetts, USA, July 30-August 2, pp. 128–137 (2006)
Har-Peled, S., Smorodinsky, S.: Conflict-free coloring of points and simple regions in the plane. Discrete and Computational Geometry 34, 47–70 (2005)
Pach, J., Toth, G.: Conflict free colorings. In: Discrete and Computational Geometry, The Goodman-Pollack Festschrift, pp. 665–671. Springer, Heidelberg (2003)
Alon, N., Smorodinsky, S.: Conflict-free colorings of shallow disks. In: Proceedings of the 22nd Annual Symposium on Computational Geometry (SCG 2006), pp. 41–43. ACM Press, New York (2006)
Bar-Noy, A., Cheilaris, P., Smorodinsky, S.: Randomized online conflict-free coloring for hypergraphs (2006) (manuscript)
Chen, K.: How to play a coloring game against a color-blind adversary. In: Proceedings of the 22nd Annual ACM Symposium on Computational Geometry (SoCG), pp. 44–51 (2006)
Fiat, A., Lev, M., Matousek, J., Mossel, E., Pach, J., Sharir, M., Smorodinsky, S., Wagner, U., Welzl, E.: Online conflict-free coloring for intervals. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 545–554 (2005)
Ajwani, D., Elbassioni, K., Govindarajan, S., Ray, S.: Conflict-free coloring for rectangle ranges using O(n.382 + ε)colors. In: Proc. 19th ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 181–187 (2007)
Bar-Noy, A., Cheilaris, P., Olonetsky, S., Smorodinsky, S.: Online conflict-free coloring for hypergraphs. Combin. Probab. Comput. 19, 493–516 (2010)
Chen, K., Kaplan, H., Sharir, M.: Online conflict-free coloring for halfplans, congruent disks, and axis-parallel rectangles. ACM Transactions on Algorithms 5(2), 16:1–16:24 (2009)
Lev-Tov, N., Peleg, D.: conflict-free coloring of unit disks. Discrete Appl. Math. 157(7), 1521–1532 (2009)
Pach, J., Tardos, G.: Conflict-free colorings of graphs and hypergraphs. Combin. Probab. Comput. 18(5), 819–834 (2009)
Smorodinsky, S.: Improved conflict-free colorings of shallow discs (2009) (manuscript)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Pira, E. (2012). Unique-Minimum Conflict-Free Coloring for a Chain of Rings. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds) Advances in Computer Science and Information Technology. Computer Science and Engineering. CCSIT 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27308-7_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-27308-7_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27307-0
Online ISBN: 978-3-642-27308-7
eBook Packages: Computer ScienceComputer Science (R0)