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).

We show that the well-known random incremental constructlon of Clarkson and Shor [14] can be adapted via gradations to provide efficient external-memory algorithms for some geomctric problems.In particular, as the main result, we obtain an optimal randomized algorithm for the problem of computing the trapezoidal decomposition determined by a set of N line scgmcnts in the plane with K pairwise intersections, that requires G($$ logMjB Q + 5) expected disk accesses (I/OS), where M is the size of the available internal memory and B is the size of the block transfer.The approach is sufficiently general to obtain algorithms for the problems of 2-d and 3-d convex hulls, 2-d abstract Voronoi diagrams and batched point location in a planar subdivision, which require an optimal expected number of I/OS and are olmplcr than the ones previously known.The results extend to a external-memory model with multiple disks.