Suffix Tree of Alignment: An Efficient Index for Similar Data

Abstract

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 +l1 leaves where l d is the sum of the lengths of all parts of B different from A and l1 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 + l1 + l2) time where l2 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 + l1 + l2) time.

Suffix Array of Alignment: A Practical Index for Similar Data

“…The suffixes of the alignment ρ, called alignment-suffixes (for short a-suffixes), are defined as in [19]. Let α a , α b , and α c be the longest suffixes of α occurring at least twice in the strings A, B, and C, respectively.…”

“…One method for constructing the SAA of ρ is using the suffix tree of the alignment ρ [19] as an intermediate index. However, this method does not make full use of the space-efficiency of suffix arrays because suffix trees require much more space than suffix arrays.…”

“…Recently, a suffix tree for similar strings, called a suffix tree of alignment [19], have been proposed without sacrificing the pattern search time, i.e., the suffix tree of alignment supports linear-time pattern search. Given an alignment of similar strings, the suffix tree of alignment stores suffixes of an alignment, called alignment-suffixes (for short a-suffixes) rather than suffixes of a string.…”

“…One might think the SAA can be simply constructed by simulating the algorithm for constructing the suffix tree of alignment in [19]. However, it is not easy because the algorithm heavily uses the dynamic property of the suffix tree and makes use of suffix links.…”

“…For this, we generalize the property dedicated to the suffix tree so that the property is satisfied in substrings of input strings. Conclusively, we can compute α * i and thus construct the SAA as efficiently as the algorithm in [19].…”