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Explicit constructions for perfect hash families

Sosina Martirosyan, Tran van Trung
2007 Designs, Codes and Cryptography  
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

Noga Alon, Shai Gutner
2010 ACM Transactions on Algorithms  
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

Noga Alon, Shai Gutner
2008 arXiv   pre-print
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

Simon R. Blackburn
2000 Journal of combinatorial theory. Series A  
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  
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]

Nader H. Bshouty
2014 arXiv   pre-print
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

Simon R Blackburn, Peter R Wild
1998 Journal of combinatorial theory. Series A  
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]

Nader H. Bshouty
2015 Lecture Notes in Computer Science  
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

Rasmus Pagh
2009 Random structures & algorithms (Print)  
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

Rasmus Pagh
2000 BRICS Report Series  
<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

S.G. Barwick, Wen-Ai Jackson
2008 Finite Fields and Their Applications  
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

Tran Van Trung, Sosina Martirosyan
2005 Designs, Codes and Cryptography  
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  
[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

Susan G. Barwick, Wen-Ai Jackson
2007 Designs, Codes and Cryptography  
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]

Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan
2012 Lecture Notes in Computer Science  
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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