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

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


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).


Service Cost Tree Decomposition Block Node Counterclockwise Order Split Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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

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