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Multi-colored Spanning Graphs

  • Hugo A. Akitaya
  • Maarten Löffler
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

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 \(k\ge 3\) and provide a \((2-\frac{1}{3+2\varrho })\)-approximation algorithm for \(k=3\) that runs in polynomial time, where \(\varrho \) 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.

Keywords

Bipartite Graph Steiner Tree Active Point Collinear Point Primary Color 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Research on this paper was supported in part by the NSF awards CCF-1422311 and CCF-1423615. Akitaya was supported by the Science Without Borders program. Löffler was partially supported by the Netherlands Organisation for Scientific Research (NWO) projects 639.021.123 and 614.001.504.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Hugo A. Akitaya
    • 1
  • Maarten Löffler
    • 2
  • Csaba D. Tóth
    • 1
    • 3
  1. 1.Tufts UniversityMedfordUSA
  2. 2.Utrecht UniversityUtrechtThe Netherlands
  3. 3.California State University NorthridgeLos AngelesUSA

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