Efficient algorithms for the weighted 2-center problem in a cactus graph

Boaz Ben-Moshe; Binay Bhattacharya; Qiaosheng Shi

doi:10.1007/11602613_70

Efficient algorithms for the weighted 2-center problem in a cactus graph

Boaz Ben-Moshe, Binay Bhattacharya, Qiaosheng Shi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

19 Scopus citations

Abstract

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n log n) 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 log ³n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log²n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log ³n). 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).

Original language	English
Title of host publication	Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings
Pages	693-703
Number of pages	11
DOIs	https://doi.org/10.1007/11602613_70
State	Published - 2005
Externally published	Yes
Event	16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China Duration: 19 Dec 2005 → 21 Dec 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3827 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Symposium on Algorithms and Computation, ISAAC 2005
Country/Territory	China
City	Hainan
Period	19/12/05 → 21/12/05

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10.1007/11602613_70

Cite this

Ben-Moshe, B., Bhattacharya, B., & Shi, Q. (2005). Efficient algorithms for the weighted 2-center problem in a cactus graph. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings (pp. 693-703). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). https://doi.org/10.1007/11602613_70

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title = "Efficient algorithms for the weighted 2-center problem in a cactus graph",

abstract = "In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n log n) 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 log 3n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log2n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log 3n). 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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Ben-Moshe, B, Bhattacharya, B & Shi, Q 2005, Efficient algorithms for the weighted 2-center problem in a cactus graph. in Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, pp. 693-703, 16th International Symposium on Algorithms and Computation, ISAAC 2005, Hainan, China, 19/12/05. https://doi.org/10.1007/11602613_70

Efficient algorithms for the weighted 2-center problem in a cactus graph. / Ben-Moshe, Boaz; Bhattacharya, Binay; Shi, Qiaosheng.
Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. 2005. p. 693-703 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ben-Moshe B, Bhattacharya B, Shi Q. Efficient algorithms for the weighted 2-center problem in a cactus graph. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. 2005. p. 693-703. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11602613_70

Efficient algorithms for the weighted 2-center problem in a cactus graph

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