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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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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