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- Ely Porat, Amir Rothschild
- IEEE Transactions on Information Theory
- 2008

Group testing is a long studied problem in combinatorics: A small set of <i>r</i> ill people should be identified out of the whole (<i>n</i> 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… (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)

- Raphaël Clifford, Klim Efremenko, Ely Porat, Amir Rothschild
- Search Methodologies
- 2009

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)

- Raphaël Clifford, Klim Efremenko, Ely Porat, Amir Rothschild
- SODA
- 2009

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)

- Raphaël Clifford, Klim Efremenko, Benny Porat, Ely Porat, Amir Rothschild
- SPIRE
- 2008

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)

- Amihood Amir, Oren Kapah, Ely Porat, Amir Rothschild
- ArXiv
- 2014

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)

- Amihood Amir, Klim Efremenko, Oren Kapah, Ely Porat, Amir Rothschild
- ArXiv
- 2008

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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