Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear-time construction algorithms and more explicit structure. We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays. The simplicity is demonstrated with a C++ implementation of 50 effective lines of code. The algorithm is called DC3, which stems from the central underlying concept of difference cover . This view leads to a generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space--time tradeoff. For any v ∈ [1, √n ], it runs in O( vn ) time using O( n / √v ) space in addition to the input string and the suffix array. We also present variants of the algorithm for several parallel and hierarchical memory models of computation. The algorithms for BSP and EREW-PRAM models are asymptotically faster than all previous suffix tree or array construction algorithms.

With the increasing amount of DNA sequence information deposited in public databases, searching for similarity to a query sequence has become a basic operation in molecular biology.But even today's fast algorithms reach their limits when applied to all-versus-all comparisons of large databases.Here we present a new database searching algorithm called QUASAR (Q-gram Alignment based on Suffix ARrays) which was designed to quickly detect sequences with strong similarity to the query in a context where many searches are conducted on one database.Our algorithm applies a modification of q-tuple filtering implemented on top of a suffix array.Two versions were developed, one for a RAM resident suffix array and one for access to the suffix array on disk.We compared our implementation with BLAST and found that our approach is an order of magnitude faster.It is, however, restricted to the search for strongly similar DNA sequences as is typically required, e.g., in the context of clustering expressed sequence tags (ESTs).