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On the NPhardness of MaxNot2
, 2012
"... We prove that, for any ɛ> 0, it is NPhard to, given a satisfiable instance of MaxNTW (Not2), find an assignment that satisfies a fraction 5 + ɛ of the constraints. This, up to the existence of ɛ, matches the 8 approximation ratio obtained by the trivial algorithm that just picks an assignment ..."
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We prove that, for any ɛ> 0, it is NPhard to, given a satisfiable instance of MaxNTW (Not2), find an assignment that satisfies a fraction 5 + ɛ of the constraints. This, up to the existence of ɛ, matches the 8 approximation ratio obtained by the trivial algorithm that just picks an assignment
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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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”
General troubleshooting is NPhard
, 2000
"... Here is the proof that decisiontheoretic troubleshooting with dependent actions is an NPhard problem, the troubleshooting with dependent costs, is NPhard too. We also present a generalization of troubleshooting that shows alternatives to minimum ECR goal function. ..."
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Here is the proof that decisiontheoretic troubleshooting with dependent actions is an NPhard problem, the troubleshooting with dependent costs, is NPhard too. We also present a generalization of troubleshooting that shows alternatives to minimum ECR goal function.
Maximizing the Cohesion is NPhard
, 2011
"... Abstract: We show that the problem of finding a set with maximum cohesion in an undirected network is NPhard. ..."
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Abstract: We show that the problem of finding a set with maximum cohesion in an undirected network is NPhard.
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
GPSGRecognition is NPHard
, 1986
"... Proponents of generalized phrase structure grammar (GPSG) cite its weak contextfree generative power as proof of the computational tractability of GPSGRecognition. Since contextfree languages (CFLs) can be parsed in time proportional to the cube of the sentence length, and GPSGs only generate CFL ..."
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recognition problem for the GPSGs of Gazdar (1981) is NPhard. Crucially, the time to parse a sentence of a CFL can be the product of sentence length cubed and contextfree grammar size squared, and the GPSG grammar can result in an exponentially large set of derived contextfree rules. A central object
Inflating Balls is NPhard
, 2008
"... A collection C of balls in R d is δinflatable if it is isometric to the intersection U ∩ E of some ddimensional affine subspace E with a collection U of (d + δ)dimensional balls that are disjoint and have equal radius. We give a quadratictime algorithm to recognize 1inflatable collections of b ..."
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of balls in any fixed dimension, and show that recognizing δinflatable collections of ddimensional balls is NPhard for δ ≥ 2 and d ≥ 3 if the balls ’ centers and radii are given by numbers of the form a + b p c + d √ e, where a,..., e are integers.
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
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