Set membership with two classical and quantum bit probes
Data Structures and Algorithms
2022-01-03 v1
Abstract
We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the bit string. Let s(m,n,t) be the minimum number of bits needed by any such scheme. We obtain new upper bounds for s(m,n,t=2), which match or improve all the previously known bounds. We also consider the quantum version of this problem and obtain improved upper bounds.
Cite
@article{arxiv.2112.14954,
title = {Set membership with two classical and quantum bit probes},
author = {Shyam Dhamapurkar and Shubham Vivek Pawar and Jaikumar Radhakrishnan},
journal= {arXiv preprint arXiv:2112.14954},
year = {2022}
}