ISAAC 2005: Algorithms and Computation pp 693-703

# Efficient Algorithms for the Weighted 2-Center Problem in a Cactus Graph

• Boaz Ben-Moshe
• Binay Bhattacharya
• Qiaosheng Shi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

## Abstract

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n logn) time algorithm is proposed that finds the weighted 1-center in a cactus graph, where n is the number of vertices in the graph. For the weighted 2-center problem, an O(n log3 n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log2 n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log3 n). This improves the previous result of O(cn) where c is the number of distinct vertex weights used in the graph [8]. In the worst case c is O(n).

## Keywords

Service Cost Tree Decomposition Block Node Counterclockwise Order Split Edge
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.

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## Authors and Affiliations

• Boaz Ben-Moshe
• 1
• Binay Bhattacharya
• 1
• Qiaosheng Shi
• 1
1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada