Abstract
We study the minimum diameter color-spanning set problem which has recently drawn some attention in the database community. We show that the problem can be solved in polynomial time for L 1 and L ∞ metrics, while it is NP-hard for all other L p metrics even in two dimensions. However, we can efficiently compute a constant factor approximation.
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References
Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristan, V.: The farthest color Voronoi diagram and related problems. In: Proceedings of the 17th European Workshop on Computational Geometry (EWCG 2001), pp. 113–116 (2001)
Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristan, V.: Smallest color-spanning objects. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 278–289. Springer, Heidelberg (2001)
Chen, Y., Chen, S., Gu, Y., Hui, M., Li, F., Liu, C., Liu, L., Ooi, B.C., Yang, X., Zhang, D., Zhou, Y.: MarcoPolo: A community system for sharing and integrating travel information on maps. In: Proceedings of the 12th International Conference on Extending Database Technology (EDBT 2009), pp. 1148–1151 (2009)
El-Gebeily, M.A., Fiagbedzi, Y.A.: On certain properties of the regular n-simplex. International Journal of Mathematical Education in Science and Technology 35(4), 617–629 (2004)
Huttenlocher, D.P., Kedem, K., Sharir, M.: The upper envelope of voronoi surfaces and its applications. Discrete & Computational Geometry, 267–291 (1993)
Jung, H.: Über die kleinste Kugel, die eine räumliche Figur einschließt. Journal für die reine und angewandte Mathematik 123, 232–257 (1901)
Zhang, D., Chee, Y.M., Mondal, A., Tung, A.K.H., Kitsuregawa, M.: Keyword search in spatial databases: Towards searching by document. In: Proceedings of the 25th IEEE International Conference on Data Engineering (ICDE 2009), pp. 688–699 (2009)
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Fleischer, R., Xu, X. (2010). Computing Minimum Diameter Color-Spanning Sets. In: Lee, DT., Chen, D.Z., Ying, S. (eds) Frontiers in Algorithmics. FAW 2010. Lecture Notes in Computer Science, vol 6213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14553-7_27
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DOI: https://doi.org/10.1007/978-3-642-14553-7_27
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