We study a problem proposed by Hurtado et al. [10] motivated by sparse set visualization. Given n points in the plane, each labeled with one or more primary colors, a colored spanning graph (CSG) is a graph such that for each primary color, the vertices of that color induce a connected subgraph. The Min-CSG problem asks for the minimum sum of edge lengths in a colored spanning graph. We show that the problem is NP-hard for k primary colors when k ≥ 3 and provide a (formula presented)-approximation algorithm for k = 3 that runs in polynomial time, where q is the Steiner ratio. Further, we give a O(n) time algorithm in the special case that the input points are collinear and k is constant.
CITATION STYLE
Akitaya, H. A., Löffler, M., & Tóth, C. D. (2016). Multi-colored spanning graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9801 LNCS, pp. 81–93). Springer Verlag. https://doi.org/10.1007/978-3-319-50106-2_7
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