Broadword Implementation of Parenthesis Queries

TL;DR

This paper introduces efficient broadword algorithms for parenthesis matching and k-th far closed parenthesis queries, achieving significant speedups on modern architectures by avoiding branches and tabulations.

Contribution

It extends broadword techniques to parenthesis queries, providing branchless, test-free algorithms with logarithmic time complexity that outperform traditional methods.

Findings

Algorithms run in O(log w) time on w-bit words.

No branch or test instructions are needed.

Significant speedup over traditional implementations.

Abstract

We continue the line of research started in "Broadword Implementation of Rank/Select Queries" proposing broadword (a.k.a. SWAR, "SIMD Within A Register") algorithms for finding matching closed parentheses and the k-th far closed parenthesis. Our algorithms work in time O(log w) on a word of w bits, and contain no branch and no test instruction. On 64-bit (and wider) architectures, these algorithms make it possible to avoid costly tabulations, while providing a very significant speedup with respect to for-loop implementations.