Update Query Time Trade-off for dynamic Suffix Arrays

TL;DR

This paper introduces a flexible data structure for dynamic suffix arrays that balances query and update times, enabling efficient string indexing and manipulation in dynamic text scenarios.

Contribution

It presents a novel data structure that supports dynamic suffix array queries and updates with tunable trade-offs, improving upon static methods for dynamic string indexing.

Findings

Supports suffix array queries in  O(n^)} time

Handles text modifications in  O(n^{1-}) time

Enables sub-linear dynamic algorithms based on suffix arrays

Abstract

The Suffix Array SA(S) of a string S[1 ... n] is an array containing all the suffixes of S sorted by lexicographic order. The suffix array is one of the most well known indexing data structures, and it functions as a key tool in many string algorithms. In this paper, we present a data structure for maintaining the Suffix Array of a dynamic string. For every $0 \leq \varepsilon \leq 1$, our data structure reports SA[i] in $\tilde{O}(n^{\varepsilon})$ time and handles text modification in $\tilde{O}(n^{1-\varepsilon})$ time. Additionally, our data structure enables the same query time for reporting iSA[i], with iSA being the Inverse Suffix Array of S[1 ... n]. Our data structure can be used to construct sub-linear dynamic variants of static strings algorithms or data structures that are based on the Suffix Array and the Inverse Suffix Array.