Longest Common Extensions in Sublinear Space

TL;DR

This paper presents a new data structure for the LCE problem that achieves a flexible trade-off between space and query time, significantly improving previous bounds and nearly matching the theoretical lower bound.

Contribution

It introduces a novel approach to solve the LCE problem with sublinear space, providing a tunable trade-off between space and query time that improves upon prior results.

Findings

Achieves $O(n/\tau)$ space and $O(\tau)$ query time for any $1 \leq \tau \leq n$

Significantly improves previous time-space trade-offs for the LCE problem

Nearly matches the known lower bound for the problem's time-space product

Abstract

The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions $i$ and $j$ in $T$. This classic problem has a well-known solution that uses $O(n)$ space and $O(1)$ query time. In this paper we show that for any trade-off parameter $1 \leq \tau \leq n$, the problem can be solved in $O(\frac{n}{\tau})$ space and $O(\tau)$ query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.