Abstract
In this paper, we describe two new explicit schemes in the bitprobe model that, to the best of our knowledge, improves upon the existing schemes in the literature. One such scheme is to store three elements using two queries in the adaptive bitprobe model. Previously, the maximum number of elements that can be handled using two queries in the adaptive model is two, which is due to Radhakrishnan et al. [2]. A corollary of this result is an explicit scheme for storing three elements using three queries in the non-adaptive model, a first such scheme in the model. The second scheme is to store four elements using four queries in the non-adaptive bitprobe model. The previous scheme to store such a configuration was a non-explicit scheme due to Alon and Fiege [1], and we provide an explicit scheme for the same.
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References
Alon, N., Feige, U.: 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, 4–6 January 2009, pp. 346–354 (2009)
Radhakrishnan, J., Raman, V., Srinivasa Rao, S.: Explicit deterministic constructions for membership in the bitprobe model. In: auf der Heide, F.M. (ed.) ESA 2001. LNCS, vol. 2161, pp. 290–299. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44676-1_24
Nicholson, P.K., Raman, V., Srinivasa Rao, S.: A survey of data structures in the bitprobe model. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds.) Space-Efficient Data Structures, Streams, and Algorithms: Papers in Honor of J. Ian Munro on the Occasion of His 66th Birthday. LNCS, vol. 8066, pp. 303–318. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40273-9_19
Garg, M., Radhakrishnan, J.: 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, 4–6 January 2015, pp. 776–784 (2015)
Blue, R.: The bit probe model for membership queries: non-adaptive bit queries. Master of Science Thesis (2009)
Kesh, D.: On adaptive bitprobe schemes for storing two elements. In: Gao, X., Du, H., Han, M. (eds.) COCOA 2017. LNCS, vol. 10627, pp. 471–479. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71150-8_39
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Baig, M.G.A.H., Kesh, D. (2018). Two New Schemes in the Bitprobe Model. In: Rahman, M., Sung, WK., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2018. Lecture Notes in Computer Science(), vol 10755. Springer, Cham. https://doi.org/10.1007/978-3-319-75172-6_7
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DOI: https://doi.org/10.1007/978-3-319-75172-6_7
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