Fully-Online Suffix Tree and Directed Acyclic Word Graph Construction for Multiple Texts

TL;DR

This paper introduces fully-online algorithms for constructing suffix trees and directed acyclic word graphs for multiple texts, allowing dynamic updates with efficient time and space complexity, suitable for real-time multi-sensor data indexing.

Contribution

It presents the first fully-online algorithms for suffix tree and DAWG construction for multiple texts with dynamic appending, extending semi-online solutions.

Findings

Constructs suffix trees and DAWGs in O(N log σ) time and O(N) space.

Provides access to updated edges via auxiliary data structures in O(log σ) time.

Handles dynamic text appending efficiently in a fully-online setting.

Abstract

We consider construction of the suffix tree and the directed acyclic word graph (DAWG) indexing data structures for a collection $\mathcal{T}$ of texts, where a new symbol may be appended to any text in $\mathcal{T} = \{T_1, \ldots, T_K\}$, at any time. This fully-online scenario, which arises in dynamically indexing multi-sensor data, is a natural generalization of the long solved semi-online text indexing problem, where texts $T_1, \ldots, T_{k}$ are permanently fixed before the next text $T_{k+1}$ is processed for each $1 \leq k < K$. We present fully-online algorithms that construct the suffix tree and the DAWG for $\mathcal{T}$ in $O(N \log \sigma)$ time and $O(N)$ space, where $N$ is the total lengths of the strings in $\mathcal{T}$ and $\sigma$ is their alphabet size. The standard explicit representation of the suffix tree leaf edges and some DAWG edges must be relaxed in our fully-online scenario, since too many updates on these edges are required in the worst case. Instead, we provide access to the updated suffix tree leaf edge labels and the DAWG edges to be redirected via auxiliary data structures, in $O(\log \sigma)$ time per added character.