A Two Query Adaptive Bitprobe Scheme Storing Five Elements
Abstract
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.
Keywords
Cite
@article{arxiv.1810.13331,
title = {A Two Query Adaptive Bitprobe Scheme Storing Five Elements},
author = {Mirza Galib Anwarul Husain Baig and Deepanjan Kesh and Chirag Sodani},
journal= {arXiv preprint arXiv:1810.13331},
year = {2019}
}
Comments
This paper is accepted for the proceeding of WALCOM 2019. It contains some of the cases which could not be added in the original paper due to page limit. Furthermore, we have added a counter example for a six element subset