Faster range minimum queries

TL;DR

This paper introduces a simple, fast-to-construct data structure for Range Minimum Queries that performs well in offline scenarios, combining it with existing solutions to achieve efficient, memory-efficient RMQ handling.

Contribution

The paper presents a new simple data structure for RMQ with fast construction and average constant query time, and combines it with existing solutions for improved performance and memory efficiency.

Findings

The proposed BbST variants are competitive with existing solutions.

The hybrid approach achieves efficient query times for wide ranges.

The data structure is memory frugal, using about 3n bits.

Abstract

Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time queries, practical performance and construction time also matter. Additionally, there are offline scenarios in which the number of queries, $q$, is rather small and given beforehand, which encourages to use a simpler approach. In this work, we present a simple data structure, with very fast construction, which allows to handle queries in constant time on average. This algorithm, however, requires access to the input data during queries (which is not the case of sophisticated RMQ solutions). We subsequently refine our technique, combining it with one of the existing succinct solutions with $O(1)$ worst-case time queries and no access to the input array. The resulting hybrid is still a memory frugal data structure, spending usually up to about $3n$ bits, and providing competitive query times, especially for wide ranges. We also show how to make our baseline data structure more compact. Experimental results demonstrate that the proposed BbST (Block-based Sparse Table) variants are competitive to existing solutions, also in the offline scenario.