ESP-Index: A Compressed Index Based on Edit-Sensitive Parsing

Abstract

We propose a compressed self-index based the edit-sensitive parsing (ESP). Given a string S, its ESP tree is equivalent to a context-free grammar deriving just S, which can be represented as a DAG G. Finding pattern P in S is reduced to embedding P into G. Succinct data structures are adopted and G is then decomposed into two LOUDS bit strings and a single array for permutation, requiring (1 + ε)nlogn + 4n + o(n) bits for any 0 < ε < 1 where n corresponds to the number of different symbols in the grammar. The time to count the occurrences of P in S is in $O(\frac{\log^*\hspace{-.9mm} u}{\varepsilon}(m\log n+occ_c(\log m\log u)))$, where m = |P|, u = |S|, and occ _c is the number of occurrences of a maximal common subtree in ESP trees of P and S. Using an additional array in n logu bits of space, our index supports locating P and displaying substring of S. Locating time is the same as counting time and displaying time for a substring of length m is O(m + logu).