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

Jaikumar Radhakrishnan, Venkatesh Raman, S. Srinivasa Rao
2001 Lecture Notes in Computer Science  
We look at time-space tradeo s 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.  ... 
doi:10.1007/3-540-44676-1_24 fatcat:qlaqa2uqqjf5plius2tgvcil4m

Data Structures for Storing Small Sets in the Bitprobe Model [chapter]

Jaikumar Radhakrishnan, Smit Shah, Saswata Shannigrahi
2010 Lecture Notes in Computer Science  
We study 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  ... 
doi:10.1007/978-3-642-15781-3_14 fatcat:eryyeherhzc7lijm7r5jhyiyqq

A Two Query Adaptive Bitprobe Scheme Storing Five Elements [article]

Mirza Galib Anwarul Husain Baig, Deepanjan Kesh, Chirag Sodani
2019 arXiv   pre-print
We are studying 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.  ... 
arXiv:1810.13331v4 fatcat:lmfrwlqkp5av7ed7kzjlwpzmrm

Pseudo-Random Graphs and Bit Probe Schemes with One-Sided Error

Andrei Romashchenko
2012 Theory of Computing Systems  
We study probabilistic bit-probe schemes 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] .  ... 
doi:10.1007/s00224-012-9425-0 fatcat:c4cczfag5nfz5ejexx676w5f24

Pseudo-random Graphs and Bit Probe Schemes with One-Sided Error [chapter]

Andrei Romashchenko
2011 Lecture Notes in Computer Science  
We study probabilistic bit-probe schemes 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] .  ... 
doi:10.1007/978-3-642-20712-9_5 fatcat:tmemdtfsajfljhlgupgzhgnvti

On the power of two, three and four probes [chapter]

Noga Alon, Uriel Feige
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.  ... 
doi:10.1137/1.9781611973068.39 fatcat:q4gvgvewsfechpnu3cegb3xzj4

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

Andrei Romashchenko
2011 arXiv   pre-print
We study probabilistic bit-probe schemes 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) .  ... 
arXiv:1102.5538v4 fatcat:mfcc7n2cnbfo3fw7kr2v6ov7oq

Randomness conductors and constant-degree lossless expanders

Michael Capalbo, Omer Reingold, Salil Vadhan, Avi Wigderson
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.  ... 
doi:10.1145/509907.510003 dblp:conf/stoc/CapalboRVW02 fatcat:aowwozdzvvapdji2f6ycmut5gq

Randomness conductors and constant-degree lossless expanders

Michael Capalbo, Omer Reingold, Salil Vadhan, Avi Wigderson
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.  ... 
doi:10.1145/510002.510003 fatcat:zrdsw422zbdtpowpnj6a4lgs3e

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

M. Capalbo, O. Reingold, S. Vadhan, A. Wigderson
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.  ... 
doi:10.1109/ccc.2002.1004327 dblp:conf/coco/CapalboRVW02 fatcat:2kfhaowwsrecxh2mkrh636zghq