Succinct Non-overlapping Indexing

Abstract

Given a text $\mathsf {T}$ having $n$ characters, we consider the non-overlapping indexing problem defined as follows: pre-process $\mathsf {T}$ into a data-structure, such that whenever a pattern $P$ comes as input, we can report a maximal set of non-overlapping occurrences of $P$ in $\mathsf {T}$. The best known solution for this problem takes linear space, in which a suffix tree of $\mathsf {T}$ is augmented with $O(n)$-word data structures. A query $P$ can be answered in optimal $O(|P|+\mathsf {nocc})$ time, where $\mathsf {nocc}$ is the output size [Cohen and Porat, ISAAC 2009]. We present the following new result: let $\mathsf {CSA}$ (not necessarily a compressed suffix array) be an index of $\mathsf {T}$ that can compute (i) the suffix range of $P$ in $\mathsf {search}(P)$ time, and (ii) a suffix array or an inverse suffix array value in $\mathsf {t_{SA}}$ time; then by using $\mathsf {CSA}$ alone, we can answer a query $P$ in $O(\mathsf {search}(P)+ \mathsf {nocc}\cdot \mathsf {t_{SA}})$ time. Additionally, we present an improved result for a generalized version of this problem called range non-overlapping indexing.

This research is funded in part by National Science Foundation (NSF) Grant CCF 1218904.