Suffix Tree of Alignment: An Efficient Index for Similar Data

TL;DR

This paper introduces a space and time-efficient suffix tree data structure for aligned similar strings, optimizing pattern search and construction by exploiting string similarities.

Contribution

It proposes a novel suffix tree of alignment that leverages string similarity to improve efficiency over traditional generalized suffix trees.

Findings

Suffix tree of alignment has fewer leaves for similar strings.

Pattern search remains efficient at O(|P|+occ) time.

Construction algorithms are optimized for different starting points.

Abstract

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.