# An Improved Scheme in the Two Query Adaptive Bitprobe Model

## TL;DR

This paper presents an improved storage scheme for small subsets in the adaptive bitprobe model, reducing space complexity from previous methods while maintaining efficient membership query responses.

## Contribution

The paper introduces a new scheme that stores subsets of size four with O(m^{5/6}) space, surpassing earlier explicit and non-explicit schemes in efficiency.

## Key findings

- Achieves O(m^{5/6}) space for storing subsets of size four
- Improves upon previous schemes with higher space complexity
- Maintains two-bit probe query efficiency

## Abstract

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.