Tight bounds for depth-two superconcentrators

Jaikumar Radhakrishnan; Amnon Ta-Shma

doi:10.1109/SFCS.1997.646148

Tight bounds for depth-two superconcentrators

Jaikumar Radhakrishnan^*
, Amnon Ta-Shma

^*Corresponding author for this work

Tata Institute

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

25 Scopus citations

Abstract

The minimum size of a depth-two N-superconcentrator is shown to be Θ(N log² N/log log N). For the upper bound, superconcentrators are developed by putting together a small number of disperser graphs. which are obtained using a probabilistic argument. Two different methods are presented to show the lower bounds. The first method shows that superconcentrators contain several disjoint disperser graphs. When combined with the lower bound for disperser graphs due to the method Kovari, Sos and Turan, this gives an almost optimal lower bound of Ω(N(log N/log log N)²) on the size of N-superconcentrators. The second method, based on the work of Hansel, gives the optimal lower bound.

Original language	English
Title of host publication	Annual Symposium on Foundations of Computer Science - Proceedings
Publisher	IEEE Comp Soc
Pages	585-594
Number of pages	10
ISBN (Print)	0818681977
DOIs	https://doi.org/10.1109/SFCS.1997.646148
State	Published - 1997
Externally published	Yes
Event	Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science - Miami Beach, FL, USA Duration: 20 Oct 1997 → 22 Oct 1997

Conference

Conference	Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science
City	Miami Beach, FL, USA
Period	20/10/97 → 22/10/97

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10.1109/SFCS.1997.646148

Cite this

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title = "Tight bounds for depth-two superconcentrators",

abstract = "The minimum size of a depth-two N-superconcentrator is shown to be Θ(N log2 N/log log N). For the upper bound, superconcentrators are developed by putting together a small number of disperser graphs. which are obtained using a probabilistic argument. Two different methods are presented to show the lower bounds. The first method shows that superconcentrators contain several disjoint disperser graphs. When combined with the lower bound for disperser graphs due to the method Kovari, Sos and Turan, this gives an almost optimal lower bound of Ω(N(log N/log log N)2) on the size of N-superconcentrators. The second method, based on the work of Hansel, gives the optimal lower bound.",

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AB - The minimum size of a depth-two N-superconcentrator is shown to be Θ(N log2 N/log log N). For the upper bound, superconcentrators are developed by putting together a small number of disperser graphs. which are obtained using a probabilistic argument. Two different methods are presented to show the lower bounds. The first method shows that superconcentrators contain several disjoint disperser graphs. When combined with the lower bound for disperser graphs due to the method Kovari, Sos and Turan, this gives an almost optimal lower bound of Ω(N(log N/log log N)2) on the size of N-superconcentrators. The second method, based on the work of Hansel, gives the optimal lower bound.

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ER -

Tight bounds for depth-two superconcentrators

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