Average complexity of exact and approximate multiple string matching

Average complexity of exact and approximate multiple string matching

We show that the average number of characters examined to search for r random patterns of length m in a text of length n over a uniformly distributed alphabet of size σ cannot be less than Ω(n log σ (rm)/m). When we permit up to k insertions, deletions, and/or substitutions of characters in the occurrences of the patterns, the lower bound becomes Ω(n(k+ log σ (rm))/m). This generalizes previous...

Average-Optimal Multiple Approximate String Matching

We present a new algorithm for multiple approximate string matching, based on an extension of the optimal (on average) singlepattern approximate string matching algorithm of Chang and Marr. Our algorithm inherits the optimality and is also competitive in practice. We present a second algorithm that is linear time and handles higher difference ratios. We show experimentally that our algorithms a...

Multiple Approximate String Matching

We present a very simple and eecient algorithm for on-line multiple approximate string matching. It uses a previously known counting-based lter 9] that searches for a single pattern by quickly discarding uninteresting parts of the text. Our multi-pattern algorithm is based on the simulation of many parallel lters using bits of the computer word. Our average complexity to search r patterns of le...

Average-Case Optimal Approximate Circular String Matching

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the...

Average-Optimal Multiple Approximate String Mat hing