Abstract
There are n points in the plane and each point is painted by one of m colors where m ≤ n. We want to select m different color points such that (1) the total edge length of resulting minimal spanning tree is as small as possible; or (2) the total edge length of resulting minimal spanning tree is as large as possible; or (3) the perimeter of the convex hull of m different color points is as small as possible. We prove NP-completeness for those three problems and give approximations algorithms for the third problem.
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References
Beresford, A.R., Stajano, F.: Location Privacy in pervasive Computing. IEEE Pervasive Computing 2(1), 46–55 (2003)
Gedik, B., Liu, L.: A customizable k-anonymity model for protecting location privacy. In: ICDCS, pp. 620–629 (2004)
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)
Das, S., Goswami, P.P., Nandy, S.C.: Smallest Color-spaning Object Revisited. International Journal of Computational Geometry and Applications (IJCGA) 19(5), 457–478 (2009)
Pfoser, D., Jensen, C.: Capturing the uncertainty of moving-objects representations. In: Proc. SSDBM, pp. 111–132 (1999)
Sistla, P.A., Wolfson, O., Chamberlain, S., Dao, S.: Querying the uncertain position of moving objects. In: Temporal Databases: Research and Practice, pp. 310–337 (1998)
Löffler, M., van Kreveld, M.: Largest and Smallest Convex Hulls for Imprecise Points. Algorithmica 56(2), 235–269 (2008)
Ju, W., Luo, J.: New Algorithms for Computing Maximum Perimeter and Maximum Area of the Convex Hull of Imprecise Inputs Based On the Parallel Line Segment Model. In: CCCG 2009, pp. 1–4 (2009)
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)
Fleischer, R., Xu, X.: Computing Minimum Diameter Color-Spanning Sets. In: Lee, D.-T., Chen, D.Z., Ying, S. (eds.) FAW 2010. LNCS, vol. 6213. Springer, Heidelberg (2010)
Borgelt, M.G., van Kreveld, M., Löffler, M., Luo, J., Merrick, D., Silveira, R.I., Vahedi, M.: Planar bichromatic minimum spanning trees. J. Discrete Algorithms 7(4), 469–478 (2009)
Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristan, V.: Smallest Color-Spanning Objects. In: Proc. 9th Annu. European Sympos. Algorithms, pp. 278–289 (2001)
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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Daescu, O., Ju, W., Luo, J. (2010). NP-Completeness of Spreading Colored Points. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_5
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DOI: https://doi.org/10.1007/978-3-642-17458-2_5
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