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 essentially G lg g bits. We introduce the first grammar-compressed index that uses O(G lg n) bits and can find the occ occurrences of patterns P [1..m] in time O((m 2 + occ) lg G). We implement the index and demonstrate its practicality in comparison with the state of the art, on highly repetitive text collections.