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Adding Unimodality or Independence Makes Interval Probability Problems NPHard
 Proceedings of the International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems IPMU’06
"... In many reallife situations, we only have partial information about probabilities. This information is usually described by bounds on moments, on probabilities of certain events, etc. – i.e., by characteristics c(p) which are linear in terms of the unknown probabilities pj. If we know interval boun ..."
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variables x1 and x2 are independent, or that for each value of x2, the corresponding conditional distribution for x1 is unimodal. We show that adding each of these conditions makes the corresponding interval probability problem NPhard. 1
The Maximum Residual Flow Problem: NPhardness With TwoArc Destruction
, 2005
"... The maximum residual flow problem with one arc destruction is shown to be solvable in strongly polynomial time in [Y.P. Aneja, R. Chandrasekaran and K.P.K. Nair, Networks, 38, 2001, 194198], however the status of the corresponding problem with more than one arc destruction is left open therein. ..."
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. We resolve the status of the twoarc destruction problem by demonstrating that it is already NPhard.
Noisy Data Make the Partial Digest Problem NPHard
"... The PARTIAL DIGEST problem wellknown for its applications in computational biology and for the intriguingly open status of its computational complexity asks for the coordinates of n points on a line such that the pairwise distances of the points form a given multiset of () distances. In an effo ..."
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Cited by 7 (1 self)
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measurements. We show that this maximization version is NPhard to approximate to within a factor of [D[ c for any e 0, where [D[ is the number of input distances, which implies that polynomialtime algorithms cannot even guarantee to find a solution for the problem that comes close to the optimum. Our
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
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 191 (2 self)
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al. (1994) introduced a Bayesian metric, called the BDe metric, that computes the relative posterior probability of a network structure given data. They show that the metric has a property desireable for inferring causal structure from data. In this paper, we show that the problem of deciding whether
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”
NPhard Optimization Problems
"... F12.24> . Given a set of variables X and a set of equations E each in k of the variables in X , nd an assignment of X . Maximize the number of equations in E that are satised by this assignment of X . Scheduling: Given a set of jobs, a processing time for each job, and a set of processors, assi ..."
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, assign the jobs to the processors. Minimize the time it takes to complete all the jobs assuming a processor can only process one job at a time. In order to prove that these are NPhard optimization problems, we must prove their corresponding decision problems are NPcomplete. For example, to prove vertex
Exact algorithms for NPhard problems: A survey
 Combinatorial Optimization  Eureka, You Shrink!, LNCS
"... Abstract. We discuss fast exponential time solutions for NPcomplete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NPcomplete problems includes the travelling salesman problem, schedu ..."
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Cited by 152 (3 self)
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Abstract. We discuss fast exponential time solutions for NPcomplete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NPcomplete problems includes the travelling salesman problem
Results 1  10
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