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Explicit constructions for perfect hash families
2007
Designs, Codes and Cryptography
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In this paper we focus on explicit constructions for perfect hash families using combinatorial methods. ...
The paper also includes extensive tables for parameters with t = 3, 4, 5, 6 of newly constructed perfect hash families. ...
Efforts have been put into searching for explicit constructions of perfect hash families. ...
doi:10.1007/s10623-007-9138-6
fatcat:vpdrxu4qfzhk5cs45kcjwz6vme
Balanced families of perfect hash functions and their applications
2010
ACM Transactions on Algorithms
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Our main result is that for any constant δ > 1, a δbalanced (n, k)-family of perfect hash functions of size 2 O(k log log k) log n can be constructed in time 2 O(k log log k) n log n. ...
The standard definition of a family of perfect hash functions requires that there will be at least one function that is 1-1 on S, for each S of size k. ...
Introduction This paper deals with explicit constructions of balanced families of perfect hash functions. ...
doi:10.1145/1798596.1798607
fatcat:yxwtjntrbzgcfo44vxkyrm2xba
Balanced Families of Perfect Hash Functions and Their Applications
2008
arXiv
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Our main result is that for any constant δ > 1, a δ-balanced (n,k)-family of perfect hash functions of size 2^O(k k) n can be constructed in time 2^O(k k) n n. ...
We say that a family of functions from [n] to [k] is a δ-balanced (n,k)-family of perfect hash functions if for every S ⊆ [n], |S|=k, the number of functions that are 1-1 on S is between T/δ and δ T for ...
The main focus of the paper is on explicit constructions of balanced families of perfect hash functions and their applications. ...
arXiv:0805.4300v1
fatcat:tmnirbqvgfba3lms6glnxebvku
Perfect Hash Families: Probabilistic Methods and Explicit Constructions
2000
Journal of combinatorial theory. Series A
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The paper also gives several explicit constructions of classes of perfect hash families. Academic Press ...
The paper presents a probabilistic existence result for perfect hash families which improves on the well known result of Mehlhorn for many parameter sets. ...
Thanks also to Peter Wild, for reading an earlier version of this paper. ...
doi:10.1006/jcta.1999.3050
fatcat:zqurqysqm5f2dbsefsvv6ru7em
Page 8663 of Mathematical Reviews Vol. , Issue 2001M
[page]
2001
Mathematical Reviews
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The goal of this work is to explore the explicit constructions
for perfect hash families from algebraic curves over finite fields.
11G_ Arithmetic algebraic geometry (Diophantine geometry)
2001m:1 1104 ...
In the last sections, they exhibit some examples to illustrate the efficiency of the constructions and, using the connections between perfect hash families and cover-free families, they obtain explicit ...
Linear time Constructions of some d-Restriction Problems
[article]
2014
arXiv
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We give new linear time globally explicit constructions for perfect hash families, cover-free families and separating hash functions. ...
We give new constructions for the following three ((1 − ǫ)-dense) drestriction problems: Perfect hash family, cover-free family and separating hash family. ...
Old and New Results
Perfect Hash Family Let H be a family of functions h : [n] → [q]. ...
arXiv:1406.2108v2
fatcat:lv4to4tbhjayhp2o5dmdfq5kem
Optimal Linear Perfect Hash Families
1998
Journal of combinatorial theory. Series A
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Perfect hash families first arose as part of database management see Mehlhorn [12] for a summary of early results. ...
Perfect hash families arise in compiler design, in circuit complexity theory and in cryptography. Let S be an (n, q, t)-perfect hash family. ...
To the best of our knowledge, the explicit linear perfect hash families in this paper are the first constructions of perfect hash families that are of smaller cardinality than the families that probabilistic ...
doi:10.1006/jcta.1998.2876
fatcat:mnk4rxcu2bfm7fok4ap7522344
Linear Time Constructions of Some $$d$$ -Restriction Problems
[chapter]
2015
Lecture Notes in Computer Science
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We give new linear time globally explicit constructions of some drestriction problems that follows from the techniques used in [1, 30, 31] . ...
We give new constructions for the following three ((1 − ǫ)-dense) drestriction problems: Perfect hash family, cover-free family and separating hash family. ...
Old and New Results
Perfect Hash Family Let H be a family of functions h : [n] → [q]. ...
doi:10.1007/978-3-319-18173-8_5
fatcat:ti5baigblrdu5jdu2xsinmyoqa
Dispersing hash functions
2009
Random structures & algorithms (Print)
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We also investigate the related issue of program size for hash functions which are nearly perfect. ...
Such families previously studied, for example universal families, are significantly larger than the smallest dispersing families, making them less suitable for derandomization. ...
Acknowledgments: The author would like to thank Martin Dietzfelbinger and Johan Kjeldgaard-Pedersen for helpful discussions, and Peter Bro Miltersen for valuable suggestions, including the possible use ...
doi:10.1002/rsa.20257
fatcat:itlak764l5hilaxzrw3pzhcala
Dispersing Hash Functions
2000
BRICS Report Series
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<br />We also investigate the related issue of program size for hash functions<br />which are nearly perfect. ...
Such families previously studied, for example <br />universal families, are significantly larger than the smallest dispersing families,<br />making them less suitable for derandomization. ...
Acknowledgments: The author would like to thank Martin Dietzfelbinger and Johan Kjeldgaard-Pedersen for helpful discussions, and Peter Bro Miltersen for valuable suggestions, including the possible use ...
doi:10.7146/brics.v7i36.20171
fatcat:kxehbgibmrex3gzqpelzaqluay
Geometric constructions of optimal linear perfect hash families
2008
Finite Fields and Their Applications
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We also give constructions of optimal linear (q 2 , q, 5)-perfect hash families. ...
In this paper we use projective geometry techniques to completely determine the values of q for which optimal linear (q 3 , q, 3)-perfect hash families exist and give constructions in these cases. ...
This gives some motivation for constructing small perfect hash families. ...
doi:10.1016/j.ffa.2007.09.003
fatcat:adshtpu6mzfhzlxvfpxnxcfv6i
New Constructions for IPP Codes
2005
Designs, Codes and Cryptography
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The first method directly constructs IPP codes, whereas the second constructs perfect hash families that are then used to derive IPP codes. ...
In this paper we consider explicit construction methods for IPP codes by means of recursion techniques. ...
If
A construction for perfect hash families and IPP codes The main result in this section is the construction of an infinite class of perfect hash families by means of a double recursive method. ...
doi:10.1007/s10623-005-6402-5
fatcat:edhboxmkuzgxxijwg6itbmid4i
Page 5766 of Mathematical Reviews Vol. , Issue 97I
[page]
1997
Mathematical Reviews
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[Wei, Wan Di] (1-NE-CS; Lincoln, NE)
Some recursive constructions for perfect hash families. (English summary)
J. Combin. Des. 4 (1996), no. 5, 353-363. ...
An (n,m, w)-perfect hash family PHF(N; n,m, w) is a set of func- tions F such that f:{1,---,n} — {1,---,m} for each f € F, |F| = N, and for any X C {1,---,m} such that |X| = w, there ex- ists at least ...
A sequence approach to linear perfect hash families
2007
Designs, Codes and Cryptography
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We develop techniques which we use to construct new optimal linear (q 2 , q, 5)-perfect hash families and (q 4 , q, 3)perfect hash families. ...
In this paper we extend the theory for linear perfect hash families based on sequences developed by Blackburn and Wild. ...
Explicit constructions of perfect hash families from algebraic curves over finite fields. J. Combin. Theory Ser A. 93 (2001) 112-124. ...
doi:10.1007/s10623-007-9091-4
fatcat:ffydjoykcvdn3bkcojlp7m6zme
Optimal Hitting Sets for Combinatorial Shapes
[chapter]
2012
Lecture Notes in Computer Science
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In the process, we construct fractional perfect hash families and hitting sets for combinatorial rectangles with stronger guarantees. These might be of independent interest. ...
We consider the problem of constructing explicit Hitting Sets for combinatorial shapes, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). ...
Acknowledgements The authors are very grateful to the anonymous referees for correcting various errors and deficiencies in an earlier version of the paper and also simplifying some of the notation and ...
doi:10.1007/978-3-642-32512-0_36
fatcat:mh3cuhkikzantnqmudcyibfkve
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