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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 finding 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 Galil–Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in(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)
A Euclidean <i>approximate sparse recovery</i> system consists of parameters k,N, an m-by-N <i>measurement matrix</i>, &#934;, and a decoding algorithm, D. Given a vector, x, the system approximates x by ^x=D(&#934; x), which must satisfy ||<sup>x</sup> - x||<sub>2</sub>&#8804; C ||x - x<sub>k</sub>||<sub>2</sub>, where x<sub>k</sub> denotes the optimal(More)
We propose Path Disruption Games (PDGs), which consider collaboration between agents attempting stop an adversary from travelling from a source node to a target node in a graph. PDGs can model physical or network security domains. The coalition attempts to stop the adversary by placing checkpoints in intermediate nodes in the graph, to make sure the(More)
We present a fully online randomized algorithm for the classical pattern matching problem that uses merely O(log m) space, breaking the O(m) barrier that held for this problem for a long time. Our method can be used as a tool in many practical applications, including monitoring Internet traffic and firewall applications. In our online model we first receive(More)
In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions for the two-dimensional substring indexing problem and the document listing problem for two patterns by reduction to the(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)
Real Scaled Matching is the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Real scaled matching is an important problem that was originally inspired by Computer Vision. In this paper, we present a new, more precise and realistic, definition for one dimensional real(More)