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NPhard
"... 92> 2 to mean that there exists a nondeterministic Turing machine M that can solve Q 1 using only polynomially many calls to a unittime oracle for solving Q 2 , each call having polynomiallybounded input. In other words, if we can solve all instances of problem Q 1 by consulting an infinitely ..."
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92> 2 to mean that there exists a nondeterministic Turing machine M that can solve Q 1 using only polynomially many calls to a unittime oracle for solving Q 2 , each call having polynomiallybounded input. In other words, if we can solve all instances of problem Q 1 by consulting
Private approximation of NPhard functions (Extended Abstract)
, 2001
"... The notion of private approximation was introduced recently by Feigenbaum, Fong, Strauss and Wright. Informally, a private approximation of a function f is another function F that approximates f in the usual sense, but does not yield any information on x other than what can be deduced from f(x). As ..."
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(x). As such, F (x) is useful for private computation of f(x) (assuming that F can be computed more efficiently than f ). In this work we examine the properties and limitations of this new notion. Specifically, we show that for many NPhard problems, the privacy requirement precludes nontrivial approximation
Learning Bayesian Networks is NPHard
, 1994
"... Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et ..."
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Cited by 194 (2 self)
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there is a Bayesian networkamong those where each node has at most k parentsthat has a relative posterior probability greater than a given constant is NPcomplete, when the BDe metric is used. 1 Introduction Recently, many researchers have begun to investigate methods for learning Bayesian networks
The approximability of NPhard problems
 In Proceedings of the Annual ACM Symposium on Theory of Computing
, 1998
"... Many problems in combinatorial optimization are NPhard (see [60]). This has forced researchers to explore techniques for dealing with NPcompleteness. Some have considered algorithms that solve “typical” ..."
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Cited by 17 (0 self)
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Many problems in combinatorial optimization are NPhard (see [60]). This has forced researchers to explore techniques for dealing with NPcompleteness. Some have considered algorithms that solve “typical”
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 683 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Polynomial Time Approximation Schemes for Dense Instances of NPHard Problems
, 1995
"... We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3satisfiabi ..."
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Cited by 189 (35 self)
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We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3
How NP Got a New Definition: A Survey of Probabilistically Checkable Proofs
, 2002
"... We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class NP, and imply that computing approximate solutions to many NPhard problems is itself NPhard. Techniques developed to prove them have had many other consequences. ..."
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Cited by 1 (0 self)
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We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class NP, and imply that computing approximate solutions to many NPhard problems is itself NPhard. Techniques developed to prove them have had many other consequences.
Local Search for NPHard Problems
, 1997
"... To date, computer scientists believe that NPHard problems cannot be solved by algorithms which run in less than exponential time in the worst case. One way to approach these problems is to design algorithms that do not guarantee a solution to every problem instance, but which solve many if not mo ..."
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Cited by 3 (0 self)
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To date, computer scientists believe that NPHard problems cannot be solved by algorithms which run in less than exponential time in the worst case. One way to approach these problems is to design algorithms that do not guarantee a solution to every problem instance, but which solve many
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
The Byzantine Generals Problem,"
 ACM Transactions on Programming Languages and Systems,
, 1982
"... Abstract The Byzantine Generals Problem requires processes to reach agreement upon a value even though some of them may fad. It is weakened by allowing them to agree upon an "incorrect" value if a failure occurs. The transaction eormmt problem for a distributed database Js a special case ..."
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Cited by 1561 (6 self)
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of the weaker problem. It is shown that, like the original Byzantine Generals Problem, the weak version can be solved only ff fewer than onethird of the processes may fad. Unlike the onginal problem, an approximate solution exists that can tolerate arbaranly many failures.
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