Designing optimal- and fast-on-average pattern matching algorithms

Designing optimal- and fast-on-average pattern matching algorithms

Given a pattern w and a text t, the speed of a pattern matching algorithm over t with regard to w, is the ratio of the length of t to the number of text accesses performed to search w into t. We first propose a general method for computing the limit of the expected speed of pattern matching algorithms, with regard to w, over iid texts. Next, we show how to determine the greatest speed which can...

Optimal pattern matching algorithms

We study a class of finite state machines, called w-matching machines, which yield to simulate the behavior of pattern matching algorithms while searching for a pattern w. They can be used to compute the asymptotic speed, i.e. the limit of the expected ratio of the number of text accesses to the length of the text, of algorithms while parsing an iid text to find the pattern w. Defining the orde...

Fast Average-Case Pattern Matching on Weighted Sequences

A weighted string over an alphabet of size σ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences, naturally arise in many contexts. In this article, we study the problem of weighted string matching with a special focus on average-case analysis. Given a weighted ...

Designing Pattern Matching Algorithms by Exploiting Structural Pattern Properties

Average-optimal string matching

The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads...