Text Indexing and Searching in Sublinear Time

We introduce the first index that can be built in o(n) time for a text of length n, and also queried in o(m) time for a pattern of length m. On a constant-size alphabet, for example, our index uses O(n log n) bits, is built in O(n/ log n) deterministic time, and finds the occ pattern occurrences in time O(m/ logn + √ logn log logn + occ), where ε > 0 is an arbitrarily small constant. As a comparison, the most recent classical text index uses O(n log n) bits, is built in O(n) time, and searches in time O(m/ logn+ log logn+occ). We build on a novel text sampling based on difference covers, which enjoys properties that allow us efficiently computing longest common prefixes in constant time. We extend our results to the secondary memory model as well, where we give the first construction in o(Sort(n)) time of a data structure with suffix array functionality, which can search for patterns in the almost optimal time, with an additive penalty of O( √ logM/B n log logn), where M is the size of main memory available and B is the disk block size. Cheriton School of Computer Science, University of Waterloo. Email [email protected]. CeBiB — Center of Biotechnology and Bioengineering, Department of Computer Science, University of Chile. Email [email protected]. Funded with Basal Funds FB0001, Conicyt, Chile. Cheriton School of Computer Science, University of Waterloo. Email: [email protected].