The effective entropy of next/previous larger/smaller value queries

TL;DR

This paper investigates the minimal bit storage needed to answer next/previous larger or smaller value queries on an array without storing the array itself, improving previous bounds.

Contribution

It presents a tighter upper bound of 3.701n bits for storing information to answer these queries, refining prior results.

Findings

Answering queries requires at most 3.701n bits

Improves previous upper bound of 4.088n bits

Provides theoretical bounds for data structure efficiency

Abstract

We study the problem of storing the minimum number of bits required to answer next/previous larger/smaller value queries on an array $A$ of $n$ numbers, without storing $A$. We show that these queries can be answered by storing at most $3.701 n$ bits. Our result improves the result of Jo and Satti [TCS 2016] that gives an upper bound of $4.088n$ bits for this problem.