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Group testing is a long studied problem in combinatorics: A small set of r ill people should be identified out of the whole (n people) by using only queries (tests) of the form " Does set X contain an ill human? ". In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This(More)
We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give an Θ (n(k + log m log k) log n) time randomised algorithm which finds(More)
We consider the classic problem of pattern matching with few mismatches in the presence of promiscuously matching wildcard symbols. Given a text t of length n and a pattern p of length m with optional wildcard symbols and a bound k, our algorithm finds all the alignments for which the pattern matches the text with Hamming distance at most k and also returns(More)
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade, several problems required efficient solution of sparse binary convolutions. Both randomized and deterministic algorithms(More)
This paper presents a new technique for deterministic length reduction. This technique improves the running time of the algorithm presented in [?] for performing fast convolution in sparse data. While the regular fast convolution of vectors V 1 , V 2 whose sizes are N 1 , N 2 respectively, takes O(N 1 log N 2) using FFT, using the new technique for length(More)
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