Constant sensitivity on the CDAWGs

TL;DR

This paper studies how the size of compact directed acyclic word graphs (CDAWGs) changes when a single character in the string is edited, showing it can increase up to eight times.

Contribution

It provides the first analysis of the sensitivity of CDAWGs to single-character edits, establishing an upper bound on size increase.

Findings

CDAWG size increases at most 8 times after an edit

The analysis applies to arbitrary positions in the string

CDAWGs are shown to be robust to small modifications

Abstract

Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string $T$ is obtained by merging isomorphic subtrees of the suffix tree [Weiner 1973] of the same string $T$, and thus CDAWGs are a compact indexing structure. In this paper, we investigate the sensitivity of CDAWGs when a single character edit operation is performed at an arbitrary position in $T$. We show that the size of the CDAWG after an edit operation on $T$ is asymptotically at most 8 times larger than the original CDAWG before the edit.