The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy sc... more The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy scenarios. Recently, Fiat and Tassa proposed a dynamic traitor tracing scenario, in which the algorithm adapts dynamically according to the responses of the pirate. Let n be the number of users and p the number of traitors.
Proceedings of the Fifth Annual Acm Siam Symposium on Discrete Algorithms, 1994
Abstract Let DCC be a dictionary. We look for efficient data structures and algorithms to solve ... more Abstract Let DCC be a dictionary. We look for efficient data structures and algorithms to solve the approximate pvery problem: Given a query u EC list all words v ED that are close to u in Hamming distance. The problem reduces to the the following combinatorial ...
Proceedings of the Fourth Annual Acm Symposium on Parallel Algorithms and Architectures, Jun 1, 1992
We present fast and e cient parallel algorithms for nding the connected components of an undirect... more We present fast and e cient parallel algorithms for nding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM.
Proceedings 41st Annual Symposium on Foundations of Computer Science, 2000
Abstract A set X of points in ℜ d is (k, b)-clusterable if X can be partitioned into k su... more Abstract A set X of points in ℜ d is (k, b)-clusterable if X can be partitioned into k subsets (clusters) so that the diameter (alternatively, the radius) of each cluster is at most b. We present algorithms that by sampling from a set X, distinguish between the case that X is (k, ...
We consider the problem of determining whether a given function ¼ ½ Ò ¼ ½ belongs to a certain cl... more We consider the problem of determining whether a given function ¼ ½ Ò ¼ ½ belongs to a certain class of Boolean functions or whether it is far from the class. More precisely, given query access to the function and given a distance parameter¯, we would like to decide whether ¾ or whether it differs from every ¾ on more than an¯-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of Ò (the number of function variables), and polynomial in the other relevant parameters.
We show how to learn monomials in the presence of malicious noise, when the underlined distributi... more We show how to learn monomials in the presence of malicious noise, when the underlined distribution is a product distribution. We show that our results apply not only to product distributions but to a wide class of distributions. 1 Introduction The Probably Approximately Correct (PAC) Learning model [Val84] has been the most widely studied model in Computational Learning Theory. From the beginning of the field, it has been considered of the utmost importance to develop algorithms that are tolerant to noise. A variety of noise models were studied. The most notable ones are the random classification noise, where the classification of the examples may be flipped randomly, and the malicious noise model, where there is no assumptions about the way in which the corrupted examples are generated. A general framework to handle noise is the Statistical Query model [K93], which was originally aimed at the random classification noise model, and later extended to the malicious noise model [D93]....
For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a p... more For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an α-approximation algorithm with an additive error for this minimization problem, if for any given additive error parameter > 0 it computes a value OPT such that, with probability at least 2/3, it holds that OPT G ≤ OPT ≤ α · OPT G + n .
For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a p... more For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an α-approximation algorithm with an additive error for this minimization problem, if for any given additive error parameter > 0 it computes a value OPT such that, with probability at least 2/3, it holds that OPT G ≤ OPT ≤ α · OPT G + n .
ABSTRACT Let D⊆Σ n be a dictionary. We look for efficient data structures and algorithms to solve... more ABSTRACT Let D⊆Σ n be a dictionary. We look for efficient data structures and algorithms to solve the following approximate query problem: Given a query u∈Σ n list all words v∈D that are close to u in Hamming distance. The problem reduces to the following combinatorial problem: Hash the vertices of the n-dimensional hypercube into buckets so that (1) the c-neighborhood of each vertex is mapped into at most k buckets and (2) no bucket is too large. Lower and upper bounds are given for the tradeoff between k and the size of the largest bucket. These results are used to derive bounds for the approximate query problem.
We present fast and e cient parallel algorithms for nding the connected components of an undirect... more We present fast and e cient parallel algorithms for nding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM.
The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy sc... more The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy scenarios. Recently, Fiat and Tassa proposed a dynamic traitor tracing scenario, in which the algorithm adapts dynamically according to the responses of the pirate. Let n be the number of users and p the number of traitors.
Convex and submodular functions play an important role in many applications, and in particular in... more Convex and submodular functions play an important role in many applications, and in particular in combinatorial optimization. Here we study two special cases: convexity in one dimension and submodularity in two dimensions. The latter type of functions are equivalent to the well-known Monge matrices.
We propose a general model for testing graph properties, which extends and simpli es the bounded ... more We propose a general model for testing graph properties, which extends and simpli es the bounded degree model of GR97]. In this model we present a family of algorithms that test whether the diameter of a graph is bounded by a given parameter D, or is -far from any graph with diameter at most (D). The function (D) ranges between D + 4 and 4D + 2, depending on the algorithm. All our algorithms run in time polynomial in 1= .
The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy sc... more The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy scenarios. Recently, Fiat and Tassa proposed a dynamic traitor tracing scenario, in which the algorithm adapts dynamically according to the responses of the pirate. Let n be the number of users and p the number of traitors.
Proceedings of the Fifth Annual Acm Siam Symposium on Discrete Algorithms, 1994
Abstract Let DCC be a dictionary. We look for efficient data structures and algorithms to solve ... more Abstract Let DCC be a dictionary. We look for efficient data structures and algorithms to solve the approximate pvery problem: Given a query u EC list all words v ED that are close to u in Hamming distance. The problem reduces to the the following combinatorial ...
Proceedings of the Fourth Annual Acm Symposium on Parallel Algorithms and Architectures, Jun 1, 1992
We present fast and e cient parallel algorithms for nding the connected components of an undirect... more We present fast and e cient parallel algorithms for nding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM.
Proceedings 41st Annual Symposium on Foundations of Computer Science, 2000
Abstract A set X of points in ℜ d is (k, b)-clusterable if X can be partitioned into k su... more Abstract A set X of points in ℜ d is (k, b)-clusterable if X can be partitioned into k subsets (clusters) so that the diameter (alternatively, the radius) of each cluster is at most b. We present algorithms that by sampling from a set X, distinguish between the case that X is (k, ...
We consider the problem of determining whether a given function ¼ ½ Ò ¼ ½ belongs to a certain cl... more We consider the problem of determining whether a given function ¼ ½ Ò ¼ ½ belongs to a certain class of Boolean functions or whether it is far from the class. More precisely, given query access to the function and given a distance parameter¯, we would like to decide whether ¾ or whether it differs from every ¾ on more than an¯-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of Ò (the number of function variables), and polynomial in the other relevant parameters.
We show how to learn monomials in the presence of malicious noise, when the underlined distributi... more We show how to learn monomials in the presence of malicious noise, when the underlined distribution is a product distribution. We show that our results apply not only to product distributions but to a wide class of distributions. 1 Introduction The Probably Approximately Correct (PAC) Learning model [Val84] has been the most widely studied model in Computational Learning Theory. From the beginning of the field, it has been considered of the utmost importance to develop algorithms that are tolerant to noise. A variety of noise models were studied. The most notable ones are the random classification noise, where the classification of the examples may be flipped randomly, and the malicious noise model, where there is no assumptions about the way in which the corrupted examples are generated. A general framework to handle noise is the Statistical Query model [K93], which was originally aimed at the random classification noise model, and later extended to the malicious noise model [D93]....
For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a p... more For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an α-approximation algorithm with an additive error for this minimization problem, if for any given additive error parameter > 0 it computes a value OPT such that, with probability at least 2/3, it holds that OPT G ≤ OPT ≤ α · OPT G + n .
For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a p... more For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an α-approximation algorithm with an additive error for this minimization problem, if for any given additive error parameter > 0 it computes a value OPT such that, with probability at least 2/3, it holds that OPT G ≤ OPT ≤ α · OPT G + n .
ABSTRACT Let D⊆Σ n be a dictionary. We look for efficient data structures and algorithms to solve... more ABSTRACT Let D⊆Σ n be a dictionary. We look for efficient data structures and algorithms to solve the following approximate query problem: Given a query u∈Σ n list all words v∈D that are close to u in Hamming distance. The problem reduces to the following combinatorial problem: Hash the vertices of the n-dimensional hypercube into buckets so that (1) the c-neighborhood of each vertex is mapped into at most k buckets and (2) no bucket is too large. Lower and upper bounds are given for the tradeoff between k and the size of the largest bucket. These results are used to derive bounds for the approximate query problem.
We present fast and e cient parallel algorithms for nding the connected components of an undirect... more We present fast and e cient parallel algorithms for nding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM.
The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy sc... more The notion of traitor tracing was introduced by Chor, Fiat and Naor, in order to combat piracy scenarios. Recently, Fiat and Tassa proposed a dynamic traitor tracing scenario, in which the algorithm adapts dynamically according to the responses of the pirate. Let n be the number of users and p the number of traitors.
Convex and submodular functions play an important role in many applications, and in particular in... more Convex and submodular functions play an important role in many applications, and in particular in combinatorial optimization. Here we study two special cases: convexity in one dimension and submodularity in two dimensions. The latter type of functions are equivalent to the well-known Monge matrices.
We propose a general model for testing graph properties, which extends and simpli es the bounded ... more We propose a general model for testing graph properties, which extends and simpli es the bounded degree model of GR97]. In this model we present a family of algorithms that test whether the diameter of a graph is bounded by a given parameter D, or is -far from any graph with diameter at most (D). The function (D) ranges between D + 4 and 4D + 2, depending on the algorithm. All our algorithms run in time polynomial in 1= .
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Papers by Michal Parnas