arXiv subjects

Deepanjan Kesh

Publications and source records attributed to Deepanjan Kesh.

4 recordsLinked to original sources

arXiv2022

Lower Bounds for Restricted Schemes in the Two-Adaptive Bitprobe Model

In the adaptive bitprobe model answering membership queries in two bitprobes, we consider the class of restricted schemes as introduced by Kesh and Sharma (Discrete Applied Mathematics 2021). In that paper, the authors showed that such restricted schemes storing subsets of size 2 require $\Omega(m^\frac{2}{3})$ space. In this paper, we generalise the result to arbitrary subsets of size $n$, and prove that the space required for such restricted schemes will be $\Omega(\left(\frac{m}{n}\right)^{1 - \frac{1}{\lfloor n / 4 \rfloor + 2}})$.

cs.DS↗

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].

cs.DS↗

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.

cs.DS↗

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.

cs.DS↗