Set Membership with Non-Adaptive Bit Probes

Authors Mohit Garg, Jaikumar Radhakrishnan



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Mohit Garg
Jaikumar Radhakrishnan

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Mohit Garg and Jaikumar Radhakrishnan. Set Membership with Non-Adaptive Bit Probes. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.STACS.2017.38

Abstract

We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S?" by non-adaptively probing the bit vector at t places. Let s_N(m,n,t) be the minimum number of bits of storage needed for such a scheme. In this work, we show existence of non-adaptive and adaptive schemes for a range of t that improves an upper bound of Buhrman, Miltersen, Radhakrishnan and Srinivasan (2002) on s_N(m,n,t). For three non-adaptive probes, we improve the previous best lower bound on s_N(m,n,3) by Alon and Feige (2009).
Keywords
  • Data Structures
  • Bit-probe model
  • Compression
  • Bloom filters
  • Expansion

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References

  1. Noga Alon and Uriel Feige. On the power of two, three and four probes. In Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, New York, NY, USA, January 4-6, 2009, pages 346-354, 2009. URL: http://dl.acm.org/citation.cfm?id=1496770.1496809.
  2. Noga Alon, Shlomo Hoory, and Nathan Linial. The Moore bound for irregular graphs. Graphs and Combinatorics, 18(1):53-57, 2002. URL: http://dx.doi.org/10.1007/s003730200002.
  3. Ajesh Babu and Jaikumar Radhakrishnan. An entropy based proof of the Moore bound for irregular graphs. CoRR, abs/1011.1058, 2010. URL: http://arxiv.org/abs/1011.1058.
  4. Harry Buhrman, Peter Bro Miltersen, Jaikumar Radhakrishnan, and Srinivasan Venkatesh. Are bitvectors optimal? SIAM J. Comput., 31(6):1723-1744, 2002. URL: http://dx.doi.org/10.1137/S0097539702405292.
  5. Mohit Garg and Jaikumar Radhakrishnan. Set membership with a few bit probes. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 776-784, 2015. URL: http://dx.doi.org/10.1137/1.9781611973730.53.
  6. Mohit Garg and Jaikumar Radhakrishnan. Set membership with non-adaptive bit probes. CoRR, abs/1612.09388, 2016. URL: http://arxiv.org/abs/1612.09388.
  7. Michael T. Goodrich and Michael Mitzenmacher. Invertible Bloom lookup tables. In 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011, Allerton Park & Retreat Center, Monticello, IL, USA, 28-30 September, 2011, pages 792-799, 2011. URL: http://dx.doi.org/10.1109/Allerton.2011.6120248.
  8. Moshe Lewenstein, J. Ian Munro, Patrick K. Nicholson, and Venkatesh Raman. Improved explicit data structures in the bitprobe model. In Algorithms - ESA 2014 - 22th Annual European Symposium, Wroclaw, Poland, September 8-10, 2014. Proceedings, pages 630-641, 2014. URL: http://dx.doi.org/10.1007/978-3-662-44777-2_52.
  9. Michael Luby, Michael Mitzenmacher, Mohammad Amin Shokrollahi, and Daniel A. Spielman. Efficient erasure correcting codes. IEEE Trans. Information Theory, 47(2):569-584, 2001. URL: http://dx.doi.org/10.1109/18.910575.
  10. Ali Makhdoumi, Shao-Lun Huang, Muriel Médard, and Yury Polyanskiy. On locally decodable source coding. In 2015 IEEE International Conference on Communications, ICC 2015, London, United Kingdom, June 8-12, 2015, pages 4394-4399, 2015. URL: http://dx.doi.org/10.1109/ICC.2015.7249014.
  11. Marvin Minsky and Seymour Papert. Perceptrons. MIT press, Cambridge, MA, 1969. Google Scholar
  12. Jaikumar Radhakrishnan, Venkatesh Raman, and S. Srinivasa Rao. Explicit deterministic constructions for membership in the bitprobe model. In Algorithms - ESA 2001, 9th Annual European Symposium, Aarhus, Denmark, August 28-31, 2001, Proceedings, pages 290-299, 2001. URL: http://dx.doi.org/10.1007/3-540-44676-1_24.
  13. Jaikumar Radhakrishnan, Pranab Sen, and Srinivasan Venkatesh. The quantum complexity of set membership. Algorithmica, 34(4):462-479, 2002. URL: http://dx.doi.org/10.1007/s00453-002-0979-0.
  14. Jaikumar Radhakrishnan, Smit Shah, and Saswata Shannigrahi. Data structures for storing small sets in the bitprobe model. In Mark de Berg and Ulrich Meyer, editors, Algorithms - ESA 2010, 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part II, volume 6347 of Lecture Notes in Computer Science, pages 159-170. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-15781-3_14.
  15. Emanuele Viola. Bit-probe lower bounds for succinct data structures. SIAM J. Comput., 41(6):1593-1604, 2012. URL: http://dx.doi.org/10.1137/090766619.
  16. Wikiversity. The 22 becs, 3-ary boolean functions - wikiversity, 2016. [Online; accessed 7-August-2016]. URL: https://en.wikiversity.org/w/index.php?title=3-ary_Boolean_functions&oldid=1587287.
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