Improved Grammar-Based Compressed Indexes

We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text T [1..u] that is represented by a (context-free) grammar of n (terminal and nonterminal) symbols and size N (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of T takes N lgn bits of space. Our representation requires 2N lgn+N lg u+ n lgn+ o(N lgn) bits of space, for any 0 < ≤ 1. It can find the positions of the occ occurrences of a pattern of length m in T in O ( (m/ ) lg ( lg u lgn ) + (m+ occ) lgn ) time, and extract any substring of length ` of T in time O(`+h lg(N/h)), where h is the height of the grammar tree.