Random Access to LZ-End: Faster and Deterministic

2026-07-16

AI Summary

This work addresses the lack of efficient, deterministic data structures for random access in LZ-End compressed texts, as existing solutions either suffer from slow queries or rely on randomization and are difficult to construct efficiently. The paper presents the first deterministic and efficiently constructible LZ-End index, combining LZ-End parsing with recursive decomposition and compact indexing. It supports single-character random access in $O(\log^2(n/z))$ time and substring extraction in $O(j - i + \log^2(n/z))$ time, all within $O(z)$ space, where $z$ is the size of the LZ-End parse. The index can be built in $O(z \log^2(n/z))$ time, offering significant improvements over prior approaches in terms of determinism, construction efficiency, and query performance.

Abstract

The LZ-End parsing of a length-$n$ string is a variation of Lempel-Ziv compression introduced by Kreft and Navarro [DCC 2010], motivated by the lack of a linear-size structure with $O(\log n)$ access time for the classical variant. While the original paper was only able to provide efficient extraction from the phrase boundaries, recently Kempa and Saha [SODA 2022] established that, for a string $S$ whose LZ-End parsing consists of $z$ phrases, there exists a random access data structure that uses $O(z)$ space and guarantees $O(\log^{4}n \cdot \log\log n)$ query time. However, their proof does not yield an efficient construction algorithm, and their data structure is inherently randomized. We resolve both limitations by providing a deterministic, $O(z)$-space data structure that supports random access queries in polylogarithmic time and can be constructed in $O(z\log^{2}(n/z))$ time directly from the LZ-End parsing. In addition to eliminating randomness and providing an efficient construction algorithm, the query time of our data structure is $O(\log^{2}(n/z))$, significantly improving upon the query time of Kempa and Saha. We also show that our techniques can be used to support the more general substring-extraction. Namely, we present a data structure with the same space and the same construction time that given two indices $i$ and $j$, outputs $S[i..j]$ in $O(j-i+\log^2\frac{n}{z})$ time.

Problem

• LZ-End
• random access
• deterministic data structure
• substring extraction
• compressed text indexing

Innovation

• LZ-End
• random access
• deterministic data structure
• substring extraction
• compressed text indexing