Grammar-compressed indexes with logarithmic search time

Abstract

Let a text T[1..n] be the only string generated by a context-free grammar with g (terminal and nonterminal) symbols, and of size G (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a grammar-compressed representation of T, can be encoded using Glg⁡G bits. We introduce the first grammar-compressed index that uses O(Glg⁡n) bits (precisely, Glg⁡n+(2+ϵ)Glg⁡g for any constant ϵ>0) and can find the occ occurrences of patterns P[1..m] in time O((m2+occ)lg⁡G). We implement the index and demonstrate its practicality in comparison with the state of the art, on highly repetitive text collections.