arXiv subjects

Mirza Galib Anwarul Husain Baig

Publications and source records attributed to Mirza Galib Anwarul Husain Baig.

4 recordsLinked to original sources

arXiv2026

Revisiting Non-Adaptive Set Membership Schemes: Removing the Logarithmic Factor

We study non-adaptive bit-probe schemes for static set membership. Each query reads a fixed number of bits and answers by strict majority. We revisit the random bipartite-graph construction of Garg and Radhakrishnan [STACS, 2017]. The main observation is that a slightly stronger expansion property already bounds the number of exceptional elements. This makes a separate probabilistic estimate for exceptional elements unnecessary. A detailed union-bound calculation then gives, for every fixed $t\ge5$, a logarithm-free existence bound of $O_t(m^{1/c}n^{1-1/c})$, where $c=\lfloor(t-1)/2\rfloor$. For odd $t$, this removes the logarithmic factor from the general upper bound of Garg and Radhakrishnan [STACS, 2017].

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arXiv2020

Improved Bounds for Two Query Adaptive Bitprobe Schemes Storing Five Elements

In this paper, we study two-bitprobe adaptive schemes storing five elements. For these class of schemes, the best known lower bound is m^{1/2} due to Alon and Feige [SODA 2009]. Recently, it was proved by Kesh [FSTTCS 2018] that two-bitprobe adaptive schemes storing three elements will take at least m^{2/3} space, which also puts a lower bound on schemes storing five elements. In this work, we have improved the lower bound to m^{3/4}. We also present a scheme for the same that takes O(m^{5/6}) space. This improves upon the O(m^{18/19})-scheme due to Garg [Ph.D. Thesis] and the O(m^{10/11})-scheme due to Baig et al. [WALCOM 2019].

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arXiv2019

A Two Query Adaptive Bitprobe Scheme Storing Five Elements

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. This result improves the non-explicit result by Garg and Radhakrishnan [2015] which takes O(m^{20/21}) space, and the explicit result by Garg [2016] which takes O(m^{18/19} ) space for the aforementioned set and query sizes.

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arXiv2018

An Improved Scheme in the Two Query Adaptive Bitprobe Model

In this paper, we look into the adaptive bitprobe model that stores subsets of size at most four from a universe of size m, and answers membership queries using two bitprobes. We propose a scheme that stores arbitrary subsets of size four using O(m^{5/6}) amount of space. This improves upon the non-explicit scheme proposed by Garg and Radhakrishnan [Garg2015] which uses O(m^{16/17}) amount of space, and the explicit scheme proposed by Garg [Thesis2015] which uses O(m^{14/15}) amount of space.

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