Fast Compressed Self-Indexes with Deterministic Linear-Time Construction

TL;DR

This paper presents a new compressed suffix array that can be built in linear deterministic time, offering efficient pattern counting with improved performance over previous indexes, suitable for large texts and alphabets.

Contribution

Introduces a compressed suffix array with deterministic linear-time construction and improved query times, outperforming existing compressed indexes in efficiency and construction time.

Findings

Constructs in $O(n)$ deterministic time

Supports pattern counting in $O(|P| + ext{loglog}_w \sigma)$ time

Outperforms previous compressed indexes in speed and space

Abstract

We introduce a compressed suffix array representation that, on a text $T$ of length $n$ over an alphabet of size $\sigma$, can be built in $O(n)$ deterministic time, within $O(n\log\sigma)$ bits of working space, and counts the number of occurrences of any pattern $P$ in $T$ in time $O(|P| + \log\log_w \sigma)$ on a RAM machine of $w=\Omega(\log n)$-bit words. This new index outperforms all the other compressed indexes that can be built in linear deterministic time, and some others. The only faster indexes can be built in linear time only in expectation, or require $\Theta(n\log n)$ bits. We also show that, by using $O(n\log\sigma)$ bits, we can build in linear time an index that counts in time $O(|P|/\log_\sigma n + \log n(\log\log n)^2)$, which is RAM-optimal for $w=\Theta(\log n)$ and sufficiently long patterns.