Multi-colored Spanning Graphs

Akitaya, Hugo A. and Löffler, Maarten and Tóth, Csaba D. (2016) Multi-colored Spanning Graphs. In: Graph Drawing and Network Visualization. GD 2016, September, 19. - 21., 2016 , pp. 81-93(Official URL: http://dx.doi.org/10.1007/978-3-319-50106-2_7).

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Abstract

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 (2−1/(3+2ϱ))-approximation algorithm for k=3 that runs in polynomial time, where ϱ 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.

Item Type: Conference Paper
Classifications: G Algorithms and Complexity > G.560 Geometry
G Algorithms and Complexity > G.070 Area / Edge Length
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1534

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