New Bounds for Perfect Hashing via Information Theory

Körner, János; Marton, Katalin

doi:10.1016/s0195-6698(88)80048-9

Cited by 90 publications

(92 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Improved lower bounds for the latter appears in [3,5,7]. For sake of completeness, we prove a weaker bound, which is sufficient for our purposes, and present the argument in probabilistic terms.…”

Section: Proof Of Theoremmentioning

confidence: 95%

On the Circuit Complexity of Perfect Hashing

Goldreich¹,

Wigderson²

2011

Studies in Complexity and Cryptography. Miscellanea on the Interplay Between Randomness and Computation

View full text Add to dashboard Cite

show abstract

Section: Proof Of Theoremmentioning

confidence: 95%

On the Circuit Complexity of Perfect Hashing

Goldreich¹,

Wigderson²

2011

Studies in Complexity and Cryptography. Miscellanea on the Interplay Between Randomness and Computation

View full text Add to dashboard Cite

show abstract

“…For r = k − 1, a slightly weaker version of this bound was proved in Fredman and Komlós (1984), and then extended to (??) by Körner and Marton (1988). All these proofs rely on certain techniques from information theory.…”

Section: Hash Functionsmentioning

confidence: 99%

Extremal Combinatorics

Jukna

2011

Texts in Theoretical Computer Science. An EATCS Series

125

View full text Add to dashboard Cite

“…An obvious necessary condition for the existence of a t-hashing family is q ≥ t; it turns out to be sufficient too (see [11], [22], [23], [29] for bounds on the rate of t-hashing families of growing length).…”

Section: Separationmentioning

confidence: 99%

“…It follows that T is 3-hashing and (3, 1)-separating from Proposition 1. The tetracode was first proved 3-hashing in [23]; combined with the (2, 2)-separation property, this yields the 2-IPP property ( [18]). …”

Section: A Variation On the Tetracodementioning

confidence: 99%

Separation and Witnesses

Cohen¹

2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We revisit two notions of difference between codewords, namely separation and the existence of small witnesses, and explore their links. IntroductionLet Q be an alphabet of size q. A subset C of Q n with |C| = M is an (n, M ) q or (n, M )-code. Elements c = (c 1 , . . . , c n ) of C are codewords. Let R = R(C) = log q M/n denote the rate of C.Coding theory asks for codes (or sets) C such that every codeword c ∈ C is as "different" as possible from all the others. The usual requirement is a large minimum Hamming distance between codewords; the associated question is to determine the maximum size of such a code.We survey here two relaxations of this problem, namely, the notions of separation and witness, and their interplay.In the first one, separation, we look for some minimum distance between disjoint subsets of codewords (instead of merely -singletons of-codewords).In the second relaxation, dealing with the existence of a witness, we look for a small subset W ⊂ [n] of coordinates such that c differs from every other codeword in W . In other words, c can be singled out from all the other codewords by observing only a small subset of coordinates.We then establish links between some separating and witness codes and conclude with a few open problems. SeparationAs an introductory illustration before the general case, consider hashing, central in Computer Science and Coding, see, e.g., [12] and its references.For a parameter t ≥ 2 a code C is called t-hashing if for any t distinct codewords c 1 , . . . , c t ∈ C there is a coordinate 1 ≤ i ≤ n such that all values cAn obvious necessary condition for the existence of a t-hashing family is q ≥ t; it turns out to be sufficient too (see [11], [22], [23], [29] for bounds on the rate of t-hashing families of growing length).An extension of hashing was introduced in [6].

show abstract

New Bounds for Perfect Hashing via Information Theory

Cited by 90 publications

References 2 publications

On the Circuit Complexity of Perfect Hashing

On the Circuit Complexity of Perfect Hashing

Extremal Combinatorics

Separation and Witnesses

Contact Info

Product

Resources

About