Suffix Array of Alignment: A Practical Index for Similar Data

Abstract

Abstract. The suffix tree of alignment is an index data structure for similar strings. Given an alignment of similar strings, it stores all suffixes of the alignment, called alignment-suffixes. An alignment-suffix represents one suffix of a string or suffixes of multiple strings starting at the same position in the alignment. The suffix tree of alignment makes good use of similarity in strings theoretically. However, suffix trees are not widely used in biological applications because of their huge space requirements, and instead suffix arrays are used in practice. In this paper we propose a space-economical version of the suffix tree of alignment, named the suffix array of alignment (SAA). Given an alignment ρ of similar strings, the SAA for ρ is a lexicographically sorted list of all the alignment-suffixes of ρ. The SAA supports pattern search as efficiently as the generalized suffix array. Our experiments show that our index uses only 14% of the space used by the generalized suffix array to index 11 human genome sequences. The space efficiency of our index increases as the number of the genome sequences increases. We also present an efficient algorithm for constructing the SAA.

On-line String Matching in Highly Similar DNA Sequences

“…It satisfies the same properties as the classical generalized su x tree by adding a new one: common su xes of two sequences are stored in an identical leaf. This result has been On-line String Matching in Highly Similar DNA Sequences extended to the su x array of an alignment [15].…”

FM-index of alignment with gaps

“…2. An alignment of similar strings can be compactly represented by combining each common substring α i in all strings as in [15,16,17]. However, the representation is not suitable for the transformed alignment Υ because the characters inα + i are not aligned in Υ.…”

“…1 Note that the definition ofα + i is different from that ofα * i in [15,16,17]. Theα + i is longer thanα * i by one.…”

“…In our index, an alignment is divided into two kinds of regions, common regions and non-common regions, and gaps in a non-common region are put together into one gap in the transformed alignment. The alignment-suffix is defined for the transformed alignment but its definition is different from those defined in [15,16,17]. Due to the alignment transformation and the new definition of the alignment-suffix, our index supports the LF-mapping and backward search, the key functionalities of the FM-index [6,7,8], regardless of gap existence in the alignment.…”

Relative Suffix Trees

“…Both the GCSA and the FMA are practical but neither support the full functionality of a suffix tree. The precursor to the FMA, the suffix tree of an alignment (STA) [ 41 , 42 ], allows certain disjunctions in the suffix tree’s edge labels in order to reduce the size of the tree while maintaining its functionality. Unlike the FMA, however, the STA has not been implemented.…”