Finding approximate repetitions under Hamming distance

Finding Approximate Repetitions under Hamming Distance

Bit-parallel approximate string matching under Hamming distance

Lossless filter for multiple repetitions with Hamming distance

Similarity search in texts, notably in biological sequences, has received substantial attention in the last few years. Numerous filtration and indexing techniques have been created in order to speed up the solution of the problem. However, previous filters were made for speeding up pattern matching, or for finding repetitions between two strings or occurring twice in the same string. In this pa...

Approximate Hamming Distance in a Stream

We consider the problem of computing a (1+ε)-approximation of the Hamming distance between a pattern of length n and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem. We show the following: If Alice and Bob both share the pattern and Alice has the first half of the stream and Bob the second half, then there is an O(ε−4 log2 n) b...

Approximate Matching with No Bound on the Hamming Distance

Recall that given a pattern p = (p1, . . . , pm) and a text t = (t1, . . . , tn), we would like to find all matches with k or fewer mismatches, meaning positions i such that |{j : pj 6= ti+j−1}| ≤ k. Any such position will be called a k-mismatch. We showed in the previous lectures how to solve this problem in O(nk) time using constant time longest common extension (LCE) operations. Here we will...