Explicit constructions of linear-sized superconcentrators

Gabber, Ofer; Galil, Zvi

doi:10.1016/0022-0000(81)90040-4

Cited by 342 publications

(170 citation statements)

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“…Thus, for example, almost every 7-regular bipartite graph has better expansion properties than the one constructed in [17]. Hence, it has been suggested by several authors (cf.…”

Section: Introductionmentioning

confidence: 97%

“…The first such construction was given by Margulis [22] and improved in [17], where a family of strong linear expanders of density 7 and expansion (2-1/3)/2 is explicitly described and used to construct a family of linear s.c.-s of density-~ 271.8. See also [3,4] for a more general construction and for better s.c.-s.…”

Section: Introductionmentioning

confidence: 99%

“…In [3] we combine similar methods with results of Kazhdan on group representations to obtain many new examples of strong linear expanders. In [5] we apply these methods together with the Fourier analysis method of [17] and the methods of [20] to obtain better explicit expanders than those previously known which enable us to construct an explicit family of linear s.c.-s of density asymptotic to 122.74, better than the previous known constructions. Finally, we have recently found a way of applying our methods to the problem of designing fault tolerant processor arrays, discussed in [29] .…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalues and expanders

1986

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Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian manifolds enables one to generate expanders randomly and check efficiently their expanding properties. It also supplies an efficient algorithm for approximating the expanding properties of a graph. The exact determination of these properties is known to be coNP-complete.

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“…Thus, for example, almost every 7-regular bipartite graph has better expansion properties than the one constructed in [17]. Hence, it has been suggested by several authors (cf.…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eigenvalues and expanders

1986

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“…The existence of linear-sized supercentrator has been proved in [4]. Since then, the size has been decreased significantly.…”

Section: Discussionmentioning

confidence: 99%

“…Gaber and Galil [4] first present a superconcentrator with O(N) edges. Following their work, the size bound became smaller and smaller.…”

Section: Introductionmentioning

confidence: 99%

Smaller Bound of Superconcentrator

Yuan

Kan

2012

IEICE Trans. Inf. & Syst.

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Tiny families of functions with random properties: A quality-size trade-off for hashing

Goldreich

Wigderson

1997

Random Struct. Alg.

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We present three explicit constructions of hash functions, which exhibit a Ž trade-off between the size of the family and hence the number of random bits needed to . Ž . generate a member of the family , and the quality or error parameter of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing propertyᎏmapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction propertyᎏmapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle, respectively, the extreme situations when the range is very large or very small. We provide lower bounds showing that our constructions are nearly optimal, and mention some applications of the new constructions. ᮊ 1997 John Ž .

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Explicit constructions of linear-sized superconcentrators

Cited by 342 publications

References 3 publications

Eigenvalues and expanders

Eigenvalues and expanders

Smaller Bound of Superconcentrator

Tiny families of functions with random properties: A quality-size trade-off for hashing

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