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

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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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).

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Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada

    Boaz Ben-Moshe, Binay Bhattacharya & Qiaosheng Shi

Authors
  1. Boaz Ben-Moshe
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  2. Binay Bhattacharya
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  3. Qiaosheng Shi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Ben-Moshe, B., Bhattacharya, B., Shi, Q. (2005). Efficient Algorithms for the Weighted 2-Center Problem in a Cactus Graph. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_70

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  • DOI: https://doi.org/10.1007/11602613_70

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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