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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 &#x201C;Does set X contain an ill human?&#x201D; In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit(More)
The string matching with mismatches problem is that of nding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Landau-Vishkin algorithm nds all locations where the pattern has at most k errors (where k is part of the input) in time(More)
The weight distribution and list-decoding size of Reed-Muller codes are studied in this work. Given a weight parameter, we are interested in bounding the number of Reed-Muller codewords with weight up to the given parameter; and given a received word and a distance parameter, we are interested in bounding the size of the list of Reed-Muller codewords that(More)
Efficient join processing is one of the most fundamental and well-studied tasks in database research. In this work, we examine algorithms for natural join queries over many relations and describe a novel algorithm to process these queries optimally in terms of worst-case data complexity. Our result builds on recent work by Atserias, Grohe, and Marx, who(More)
We give a space-optimal streaming algorithm with update time O(log<sup>2</sup>(1/&#949;)loglog(1/&#949;)) for approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream up to a factor of 1 +/- &#949;. This provides a nearly exponential improvement over the previous space optimal algorithm of [Kane-Nelson-Woodruff, SODA(More)
Historically, approximate pattern matching has mainly focused at coping with errors in the data, while the order of the text/pattern was assumed to be more or less correct. In this paper we consider a class of pattern matching problems where the content is assumed to be correct, while the <i>locations</i> may have shifted/changed. We formally define a broad(More)
We introduce a new matching criterion – function matching – that captures several different applications. The function matching problem has as its input a text T of length n over alphabet ΣT and a pattern P = P [1]P [2] · · · P [m] of length m over alphabet ΣP. We seek all text locations i for which, for some function f : ΣP → ΣT (f may also depend on i),(More)