Faster Algorithms for the Minimum Red-Blue-Purple Spanning Graph Problem

Authors

  • Ahmad Biniaz
  • Prosenjit Bose
  • Ingo van Duijn
  • Anil Maheshwari
  • Michiel Smid

DOI:

https://doi.org/10.7155/jgaa.00427

Keywords:

red-blue-purple points , minimum spanning graph , points on cirle

Abstract

Consider a set of $n$ points in the plane, each one of which is colored either red, blue, or purple. A red-blue-purple spanning graph (RBP spanning graph) is a graph whose vertices are the points and whose edges connect the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. The minimum RBP spanning graph problem is to find an RBP spanning graph with minimum total edge length. First we consider this problem for the case when the points are located on a circle. We present an algorithm that solves this problem in $O(n^2)$ time, improving upon the previous algorithm by a factor of $\Theta(n)$. Also, for the general case we present an algorithm that runs in $O(n^5)$ time, improving upon the previous algorithm by a factor of $\Theta(n)$.

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Published

2024-03-16

How to Cite

Biniaz, A., Bose, P., van Duijn, I., Maheshwari, A., & Smid, M. (2024). Faster Algorithms for the Minimum Red-Blue-Purple Spanning Graph Problem. Journal of Graph Algorithms and Applications, 21(4), 527–546. https://doi.org/10.7155/jgaa.00427

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