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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 give the first non-trivial algorithms 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 O(n(k + log n log log n) log m) time randomised… (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)

We consider the well known problem of pattern matching under the Hamming distance. Previous approaches have shown how to count the number of mismatches efficiently especially, when a bound is known for the maximum Hamming distance. Our interest is different in that we wish collect a random sample of mismatches of fixed size at each position in the text.… (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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