From independence to expansion and back again

Tobias Lybecker Christiani; Rasmus Pagh; Mikkel Thorup

doi:10.1145/2746539.2746620

From independence to expansion and back again

Tobias Lybecker Christiani, Rasmus Pagh, Mikkel Thorup

Datalogisk Institut

8 Citationer (Scopus)

Abstract

We consider the following fundamental problems: • Constructing k-independent hash functions with a spacetime tradeoff close to Siegel's lower bound. • Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function. It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel's lower bound, our time bound is just a logarithmic factor from the lower bound.

Originalsprog	Engelsk
Titel	Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing : STOC '15
Antal sider	8
Forlag	Association for Computing Machinery
Publikationsdato	14 jun. 2015
Sider	813-820
ISBN (Trykt)	978-1-4503-3536-2
DOI	https://doi.org/10.1145/2746539.2746620
Status	Udgivet - 14 jun. 2015
Begivenhed	Annual ACM Symposium on the Theory of Computing 2015 - Portland, USA Varighed: 15 jun. 2015 → 17 jun. 2015 Konferencens nummer: 47

Konference

Konference	Annual ACM Symposium on the Theory of Computing 2015
Nummer	47
Land/Område	USA
By	Portland
Periode	15/06/2015 → 17/06/2015

Emneord

bipartite expanders, hash functions, k-independence

Adgang til dokumentet

10.1145/2746539.2746620

http://doi.acm.org/10.1145/2746539.2746620

Citationsformater

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title = "From independence to expansion and back again",

abstract = "We consider the following fundamental problems: • Constructing k-independent hash functions with a spacetime tradeoff close to Siegel's lower bound. • Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function. It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel's lower bound, our time bound is just a logarithmic factor from the lower bound.",

keywords = "bipartite expanders, hash functions, k-independence",

author = "Christiani, {Tobias Lybecker} and Rasmus Pagh and Mikkel Thorup",

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booktitle = "Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing",

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note = "Annual ACM Symposium on the Theory of Computing 2015, STOC '15 ; Conference date: 15-06-2015 Through 17-06-2015",

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T1 - From independence to expansion and back again

AU - Christiani, Tobias Lybecker

AU - Pagh, Rasmus

AU - Thorup, Mikkel

N1 - Conference code: 47

PY - 2015/6/14

Y1 - 2015/6/14

N2 - We consider the following fundamental problems: • Constructing k-independent hash functions with a spacetime tradeoff close to Siegel's lower bound. • Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function. It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel's lower bound, our time bound is just a logarithmic factor from the lower bound.

AB - We consider the following fundamental problems: • Constructing k-independent hash functions with a spacetime tradeoff close to Siegel's lower bound. • Constructing representations of unbalanced expander graphs having small size and allowing fast computation of the neighbor function. It is not hard to show that these problems are intimately connected in the sense that a good solution to one of them leads to a good solution to the other one. In this paper we exploit this connection to present efficient, recursive constructions of k-independent hash functions (and hence expanders with a small representation). While the previously most efficient construction (Thorup, FOCS 2013) needed time quasipolynomial in Siegel's lower bound, our time bound is just a logarithmic factor from the lower bound.

KW - bipartite expanders, hash functions, k-independence

U2 - 10.1145/2746539.2746620

DO - 10.1145/2746539.2746620

M3 - Article in proceedings

SN - 978-1-4503-3536-2

SP - 813

EP - 820

BT - Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing

PB - Association for Computing Machinery

T2 - Annual ACM Symposium on the Theory of Computing 2015

Y2 - 15 June 2015 through 17 June 2015

ER -

From independence to expansion and back again

Abstract

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Citationsformater