Fast maintenance of rectilinear centers

Sergei Bespamyatnikh; Michael Segal

doi:10.1007/3-540-45545-0_73

Fast maintenance of rectilinear centers

Sergei Bespamyatnikh
, Michael Segal

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

Abstract

We address the problem of dynamic maintenance of 2-centers in the plane under rectilinear metric.We present two algorithms for the continuous and discrete ver- sions of the problem. We show that rectilinear 2-centers can be maintained in O(log² n) time. We give an algorithm for semi-dynamic (either insertions only or deletions only) maintenance of the discrete 2-centers in O(log n logm) amortized time where n is the number of customer points and m is the number of possible locations of centers.

Original language	English
Title of host publication	Computational Science - ICCS 2001 - International Conference, 2001, Proceedings
Editors	Vassil N. Alexandrov, Jack J. Dongarra, Benjoe A. Juliano, René S. Renner, C.J. Kenneth Tan
Publisher	Springer Verlag
Pages	633-639
Number of pages	7
ISBN (Print)	3540422323, 9783540422327
DOIs	https://doi.org/10.1007/3-540-45545-0_73
State	Published - 1 Jan 2001
Event	International Conference on Computational Science, ICCS 2001 - San Francisco, United States Duration: 28 May 2001 → 30 May 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2073
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Conference on Computational Science, ICCS 2001
Country/Territory	United States
City	San Francisco
Period	28/05/01 → 30/05/01

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/3-540-45545-0_73

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Bespamyatnikh, S., & Segal, M. (2001). Fast maintenance of rectilinear centers. In V. N. Alexandrov, J. J. Dongarra, B. A. Juliano, R. S. Renner, & C. J. Kenneth Tan (Eds.), Computational Science - ICCS 2001 - International Conference, 2001, Proceedings (pp. 633-639). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2073). Springer Verlag. https://doi.org/10.1007/3-540-45545-0_73

Bespamyatnikh, Sergei ; Segal, Michael. / Fast maintenance of rectilinear centers. Computational Science - ICCS 2001 - International Conference, 2001, Proceedings. editor / Vassil N. Alexandrov ; Jack J. Dongarra ; Benjoe A. Juliano ; René S. Renner ; C.J. Kenneth Tan. Springer Verlag, 2001. pp. 633-639 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We address the problem of dynamic maintenance of 2-centers in the plane under rectilinear metric.We present two algorithms for the continuous and discrete ver- sions of the problem. We show that rectilinear 2-centers can be maintained in O(log2 n) time. We give an algorithm for semi-dynamic (either insertions only or deletions only) maintenance of the discrete 2-centers in O(log n logm) amortized time where n is the number of customer points and m is the number of possible locations of centers.",

author = "Sergei Bespamyatnikh and Michael Segal",

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Bespamyatnikh, S & Segal, M 2001, Fast maintenance of rectilinear centers. in VN Alexandrov, JJ Dongarra, BA Juliano, RS Renner & CJ Kenneth Tan (eds), Computational Science - ICCS 2001 - International Conference, 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2073, Springer Verlag, pp. 633-639, International Conference on Computational Science, ICCS 2001, San Francisco, United States, 28/05/01. https://doi.org/10.1007/3-540-45545-0_73

Fast maintenance of rectilinear centers. / Bespamyatnikh, Sergei; Segal, Michael.
Computational Science - ICCS 2001 - International Conference, 2001, Proceedings. ed. / Vassil N. Alexandrov; Jack J. Dongarra; Benjoe A. Juliano; René S. Renner; C.J. Kenneth Tan. Springer Verlag, 2001. p. 633-639 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2073).

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

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N2 - We address the problem of dynamic maintenance of 2-centers in the plane under rectilinear metric.We present two algorithms for the continuous and discrete ver- sions of the problem. We show that rectilinear 2-centers can be maintained in O(log2 n) time. We give an algorithm for semi-dynamic (either insertions only or deletions only) maintenance of the discrete 2-centers in O(log n logm) amortized time where n is the number of customer points and m is the number of possible locations of centers.

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SN - 9783540422327

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Bespamyatnikh S, Segal M. Fast maintenance of rectilinear centers. In Alexandrov VN, Dongarra JJ, Juliano BA, Renner RS, Kenneth Tan CJ, editors, Computational Science - ICCS 2001 - International Conference, 2001, Proceedings. Springer Verlag. 2001. p. 633-639. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45545-0_73

Fast maintenance of rectilinear centers

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