An Opportunistic Text Indexing Structure Based on Run Length Encoding

Abstract

We present a new text indexing structure based on the run length encoding (RLE) of a text string $T$ which, given the RLE of a query pattern $P$, reports all the $occ$ occurrences of $P$ in $T$ in $O(m + occ + \log n)$ time, where $n$ and $m$ are the sizes of the RLEs of $T$ and $P$, respectively. The data structure requires $n (2\log N + \log n + \log \sigma ) + O(n)$ bits of space, where $N$ is the length of the uncompressed text string $T$ and $\sigma$ is the alphabet size. Moreover, using $n (3\log N + \log n + \log \sigma ) + 2 \sigma \log \frac{N}{\sigma } + O(n \log \log n)$ bits of total space, our data structure can be enhanced to answer the beginning position of the lexicographically $i$th smallest suffix of $T$ for a given rank $i$ in $O(\log ^2 n)$ time. All these data structures can be constructed in $O(n \log n)$ time using $O(n \log N)$ bits of extra space.