Suffix tree of alignment: An efficient index for similar data

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.