Compact and hash based variants of the suffix array

Abstract

1 By the latter we mean indexes with space bounded by O (nH 0 ) or even O (nH k ) bits, where n is the text length, and H 0 (H k ) the order-0 (order-k) entropy. The former term, compact full-text indexes, is less definite, and may fit any structure with less than nlog 2 n bits of space, at least for ՚՚typical՚՚ texts. * e-mail: sgrabow@kis.p.lodz.pl Manuscript submitted 2016Manuscript submitted -11-01, revised 2016 One may define a full-text index over text T of length n as a data structure supporting at least two types of queries, both with respect to a pattern P of length m, where T and P share an integer alphabet of size σ. One query type is count: return the number occ ¸ 0 of occurrences of P in T. The other query type is locate: for each pattern occurrence report its position in T, that is, such j thatThe suffix Related workThe full-text indexing history starts with the suffix tree (ST) [7], a trie whose string collection is the set of all the suffixes of a given text, with an additional requirement that all nonbranching paths of edges are converted into single edges. Each ST path is terminated as soon as it points to a unique suffix, whose start position is kept in the corresponding leaf. As there are n leaves, up to n ¡ 1 internal nodes (as each internal node must have at least two children) and edge labels are represented with pointers to the text, it is easy to see that the suffix tree takes O(n) words of space, i.e., O(nlogn) bits.Suffix trees can be built in linear time for integer alphabets [8]. Assuming constant-time access to any child of a given node, the search in the ST takes only O(m + occ) time in the worst case. In practice, this is cumbersome for a large alphabet, of size n ω(1) , as it requires using perfect hashing, which also makes the construction time linear only in expectation. A small alphabet is easier to handle, which is one of the reasons of the wide use of suffix trees in bioinformatics.

DNA-protein quasi-mapping for rapid differential gene expression analysis in non-model organisms

“…The role of HT is to allow faster searches in SA by reducing the search area of binary search. This idea has been explored in greater detail in [8]. Additionally, we construct a bit vector B of the same length as C containing 1 at each position corresponding to the special character $ and 0 elsewhere.…”