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Explicit Deterministic Constructions for Membership in the Bitprobe Model
[chapter]

2001
*
Lecture Notes in Computer Science
*

We look at time-space tradeo s

doi:10.1007/3-540-44676-1_24
fatcat:qlaqa2uqqjf5plius2tgvcil4m
*for**the*static*membership*problem*in**the*bit-probe*model*. ... We show several*deterministic*upper bounds*for**the*case when*the*number of bit probes, is small, by*explicit**constructions*, culminating*in*one that uses o(m) bits of space where*membership*can be determined ... Part of*the*work was done while*the*second author was visiting*the*University of Waterloo, Canada. He thanks Ian Munro and Erik Demaine*for*useful discussions. ...##
###
Data Structures for Storing Small Sets in the Bitprobe Model
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-642-15781-3_14
fatcat:eryyeherhzc7lijm7r5jhyiyqq
*the*following set*membership*problem*in**the*bit probe*model*: given a set S from a finite universe U , represent it*in*memory so that*membership*queries of*the*form "Is x*in*S?" ... can be answered with a small number of*bitprobes*. We obtain*explicit*schemes that come close to*the*information theoretic lower bound of Buhrman et al. ... It is easy to see that this argument works*for*other AND-type functions and*for*f 1 . 2 Concluding remarks We have studied*the*set*membership*problem*in**the**bitprobe**model*with*the*aim of determining ...##
###
A Two Query Adaptive Bitprobe Scheme Storing Five Elements
[article]

2019
*
arXiv
*
pre-print

We are studying

arXiv:1810.13331v4
fatcat:lmfrwlqkp5av7ed7kzjlwpzmrm
*the*adaptive*bitprobe**model*to store an arbitrary subset S of size at most five from a universe U of size m and answer*the**membership*queries of*the*form "Is x*in*S?" ...*in*two*bitprobes*.*In*this paper, we present a data structure*for**the*aforementioned problem. Our data structure takes O(m^10/11) space. ... .:*Explicit**deterministic**constructions**for**membership**in**the**bitprobe**model*.*In*: European Symposium on Algorithms. pp. 290-299. Springer (2001) 13. ...##
###
Pseudo-Random Graphs and Bit Probe Schemes with One-Sided Error

2012
*
Theory of Computing Systems
*

We study probabilistic bit-probe schemes

doi:10.1007/s00224-012-9425-0
fatcat:c4cczfag5nfz5ejexx676w5f24
*for**the**membership*problem. Given a set A of at most n elements from*the*universe of size m we organize such a structure that queries of type "x ∈ A?" ...*The**constructions**in*[15] is not*explicit*: given*the*list of elements A,*the*corresponding scheme is*constructed*(with some brute force search)*in*time 2 poly(m) . ... However,*in**the*BMRV-scheme we need a graph where*the*right part of*the*graph is much less than*the*left part. Some*explicit**construction*suitable*for*BMRV-scheme was suggested*in*[18] . ...##
###
Pseudo-random Graphs and Bit Probe Schemes with One-Sided Error
[chapter]

2011
*
Lecture Notes in Computer Science
*

We study probabilistic bit-probe schemes

doi:10.1007/978-3-642-20712-9_5
fatcat:tmemdtfsajfljhlgupgzhgnvti
*for**the**membership*problem. Given a set A of at most n elements from*the*universe of size m we organize such a structure that queries of type "x ∈ A?" ...*The**constructions**in*[15] is not*explicit*: given*the*list of elements A,*the*corresponding scheme is*constructed*(with some brute force search)*in*time 2 poly(m) . ... However,*in**the*BMRV-scheme we need a graph where*the*right part of*the*graph is much less than*the*left part. Some*explicit**construction*suitable*for*BMRV-scheme was suggested*in*[18] . ...##
###
On the power of two, three and four probes
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

*The*study of such schemes arises

*in*

*the*investigation of

*the*static

*membership*problem

*in*

*the*

*bitprobe*

*model*. ... An adaptive (n, m, s, t)-scheme is a

*deterministic*scheme

*for*encoding a vector X of m bits with at most n ones by a vector Y of s bits, so that any bit of X can be determined by t adaptive probes to Y ... Acknowledgements We thank Bill Gasarch and Matt McCutchen

*for*their useful comments on an earlier version of this manuscript. ...

##
###
Pseudo-random graphs and bit probe schemes with one-sided error
[article]

2011
*
arXiv
*
pre-print

We study probabilistic bit-probe schemes

arXiv:1102.5538v4
fatcat:mfcc7n2cnbfo3fw7kr2v6ov7oq
*for**the**membership*problem. Given a set A of at most n elements from*the*universe of size m we organize such a structure that queries of type "Is x*in*A?" ...*In*this paper we show that*for**the*same problem there exists a bit-probe scheme with one-sided error that needs space of O(n^2 m+( m)) bits. ...*The**constructions**in*[18] is not*explicit*: given*the*list of elements A,*the*corresponding scheme is*constructed*(with some brute force search)*in*time 2 poly(m) . ...##
###
Randomness conductors and constant-degree lossless expanders

2002
*
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02
*

*The*best previous

*explicit*

*constructions*gave expansion factor D/2, which is too weak

*for*many applications. ...

*The*main concrete result of this paper is

*the*first

*explicit*

*construction*of constant degree lossless expanders. ... discussions about

*the*applications to codes, and

*the*referees

*for*helpful comments on

*the*presentation. ...

##
###
Randomness conductors and constant-degree lossless expanders

2002
*
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02
*

*The*best previous

*explicit*

*constructions*gave expansion factor D/2, which is too weak

*for*many applications. ...

*The*main concrete result of this paper is

*the*first

*explicit*

*construction*of constant degree lossless expanders. ... discussions about

*the*applications to codes, and

*the*referees

*for*helpful comments on

*the*presentation. ...

##
###
Page 1703 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

*Explicit*

*deterministic*

*constructions*

*for*

*membership*

*in*

*the*

*bitprobe*

*model*. (English summary) A/gorithms—ESA 2001 (Arhus), 290-299, Lecture Notes

*in*Comput. Sci., 2161, Springer, Berlin, 2001. ... (Introduction) 2003d:62147 62H30 — (with SuSinskas, Jurgis) Comparison of Poisson mixture

*models*

*for*count data clusterization. ...

##
###
Randomness conductors and constant-degree lossless expanders

*
Proceedings 17th IEEE Annual Conference on Computational Complexity
*

*The*best previous

*explicit*

*constructions*gave expansion factor D/2, which is too weak

*for*many applications. ...

*The*main concrete result of this paper is

*the*first

*explicit*

*construction*of constant degree lossless expanders. ... discussions about

*the*applications to codes, and

*the*referees

*for*helpful comments on

*the*presentation. ...