Faster batched range minimum queries

TL;DR

This paper improves the efficiency of batch range minimum queries by adapting sparse table techniques and proposing a new variant that trades space for speed, especially effective for small query batches.

Contribution

It introduces a faster method for small batch RMQ by adapting sparse tables to blocks and proposes a space-intensive variant without array contraction.

Findings

Speedup of 3.8--7.8 times over previous methods

Effective for small, known query batches

New block-based sparse table adaptation

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, there are scenarios in which the number of queries, $q$, is rather small and given beforehand, which encourages to use a simpler approach. A recent work by Alzamel et al. starts with contracting the input array to a much shorter one, with its size proportional to $q$. In this work, we build upon their solution, speeding up handling small batches of queries by a factor of 3.8--7.8 (the gap grows with $q$). The key idea that helped us achieve this advantage is adapting the well-known Sparse Table technique to work on blocks, with speculative block minima comparisons. We also propose an even much faster (but possibly using more space) variant without the array contraction.