Bit-parallel string matching under Hamming distance in O(n[m/w]) worst case time

Practical and Optimal String Matching

We develop a new exact bit-parallel string matching algorithm, based on the Shift-Or algorithm (Baeza-Yates & Gonnet, 1992). Assuming that the pattern representation fits into a single computer word, this algorithm has optimal O(n logσ m/m) average running time, as well as optimal O(n) worst case running time, where n, m and σ are the sizes of the text, the pattern, and the alphabet, respective...

Bit-parallel approximate string matching under Hamming distance

On the inverse maximum perfect matching problem under the bottleneck-type Hamming distance

Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...

Efficient Bit-parallel Algorithms for (δ, α)-matching

We consider the following string matching problem. Pattern p0p1p2 . . . pm−1 (δ, α)-matches the text substring ti0 ti1ti2 . . . tim−1 , if |pj − tij | ≤ δ for j ∈ {0, . . . , m− 1}, where 0 < ij+1 − ij ≤ α + 1. The task is then to find all text positions im−1 that (δ, α)-match the pattern. For a text of length n, the best previously known algorithms for this string matching problem run in time ...

Bit-parallel (δ, γ)-Matching and Suffix Automata

(δ, γ )-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P1...m and a text T1...n on an alphabet of integers, find the occurrences P ′ of the pattern in the text such that (i) ∀1 i m, |Pi−P ′ i | δ, and (ii) ∑ 1 i m |Pi−P ′ i | γ . The problem makes sense for δ γ δm. Several techniques for (δ, γ )-matching have been proposed, based on bit-...