Selection networks with 8n log2n size and O(log n) depth

Shuji Jimbo; Akira Maruoka

doi:10.1007/3-540-56279-6_69

Selection networks with 8n log₂n size and O(log n) depth

Shuji Jimbo, Akira Maruoka

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

1 Citation (Scopus)

Abstract

An (n, n/2)-selector is a comparator network that classifies a set of n values into two classes with the same number of values in such a way that each element in one class is at least as large as all of those in the other. Based on utilization of expanders, Pippenger[6] constructed (n, n/2)-selectors, whose size is asymptotic to 2n log₂ n and whose depth is O((log n)²). In the same spirit, we obtain a relatively simple method to construct (n, n/2)-seleetors of depth O(log n). We construct (n, n/2)-selectors of size at most 8n log ₂ n + O(n). Moreover, for arbitrary C > 3/log₂ 3 = 1.8927…, we construct (n, n/2)-selectors of size at most Cn log₂n + O(n).

Original language	English
Title of host publication	Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings
Editors	Takao Nishizeki, Toshihide Ibaraki, Kazuo Iwama, Masafurni Yamashita, Yasuyoshi Inagaki
Publisher	Springer Verlag
Pages	165-174
Number of pages	10
ISBN (Print)	9783540562795
DOIs	https://doi.org/10.1007/3-540-56279-6_69
Publication status	Published - 1992
Externally published	Yes
Event	3rd International Symposium on Algorithms and Computation, ISAAC 1992 - Nagoya, Japan Duration: Dec 16 1992 → Dec 18 1992

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	650 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	3rd International Symposium on Algorithms and Computation, ISAAC 1992
Country	Japan
City	Nagoya
Period	12/16/92 → 12/18/92

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-56279-6_69

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Cite this

Jimbo, S., & Maruoka, A. (1992). Selection networks with 8n log₂n size and O(log n) depth. In T. Nishizeki, T. Ibaraki, K. Iwama, M. Yamashita, & Y. Inagaki (Eds.), Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings (pp. 165-174). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 650 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-56279-6_69

Selection networks with 8n log₂n size and O(log n) depth. / Jimbo, Shuji; Maruoka, Akira.

Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings. ed. / Takao Nishizeki; Toshihide Ibaraki; Kazuo Iwama; Masafurni Yamashita; Yasuyoshi Inagaki. Springer Verlag, 1992. p. 165-174 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 650 LNCS).

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

Jimbo, S & Maruoka, A 1992, Selection networks with 8n log₂n size and O(log n) depth. in T Nishizeki, T Ibaraki, K Iwama, M Yamashita & Y Inagaki (eds), Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 650 LNCS, Springer Verlag, pp. 165-174, 3rd International Symposium on Algorithms and Computation, ISAAC 1992, Nagoya, Japan, 12/16/92. https://doi.org/10.1007/3-540-56279-6_69

Jimbo S, Maruoka A. Selection networks with 8n log₂n size and O(log n) depth. In Nishizeki T, Ibaraki T, Iwama K, Yamashita M, Inagaki Y, editors, Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings. Springer Verlag. 1992. p. 165-174. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-56279-6_69

Jimbo, Shuji ; Maruoka, Akira. / Selection networks with 8n log₂n size and O(log n) depth. Algorithms and Computation - 3rd International Symposium, ISAAC 1992, Proceedings. editor / Takao Nishizeki ; Toshihide Ibaraki ; Kazuo Iwama ; Masafurni Yamashita ; Yasuyoshi Inagaki. Springer Verlag, 1992. pp. 165-174 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "An (n, n/2)-selector is a comparator network that classifies a set of n values into two classes with the same number of values in such a way that each element in one class is at least as large as all of those in the other. Based on utilization of expanders, Pippenger[6] constructed (n, n/2)-selectors, whose size is asymptotic to 2n log2 n and whose depth is O((log n)2). In the same spirit, we obtain a relatively simple method to construct (n, n/2)-seleetors of depth O(log n). We construct (n, n/2)-selectors of size at most 8n log 2 n + O(n). Moreover, for arbitrary C > 3/log2 3 = 1.8927…, we construct (n, n/2)-selectors of size at most Cn log2n + O(n).",

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