Faster subsequence recognition in compressed strings

TL;DR

This paper presents an improved algorithm for local subsequence recognition in compressed strings, reducing the time complexity from quadratic to near-linear in the pattern length, enabling more efficient processing of massive data sets.

Contribution

The authors develop a faster algorithm for subsequence recognition on SLP-compressed strings, improving the time complexity from O(𝑚̄ n^2 log n) to O(𝑚̄ n^{1.5}), and extend it to compute longest common subsequences.

Findings

Algorithm runs in O(𝑚̄ n^{1.5}) time for subsequence recognition.

Extension to longest common subsequence computation in similar time.

Improves efficiency for processing large compressed data sets.

Abstract

Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to Lempel--Ziv compression. For an SLP-compressed text of length $\bar m$, and an uncompressed pattern of length $n$, C{\'e}gielski et al. gave an algorithm for local subsequence recognition running in time $O(\bar mn^2 \log n)$. We improve the running time to $O(\bar mn^{1.5})$. Our algorithm can also be used to compute the longest common subsequence between a compressed text and an uncompressed pattern in time $O(\bar mn^{1.5})$; the same problem with a compressed pattern is known to be NP-hard.