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A general method to speed up fixed-parameter-tractable algorithms

Rolf Niedermeier, Peter Rossmanith
2000 Information Processing Letters  
A fixed-parameter-tractable algorithm, or FPT algorithm for short, gets an instance (I, k) as its input and has to decide whether (I, k) ∈ L for some parameterized problem L.  ...  Many parameterized algorithms work in two stages: reduction to a problem kernel and bounded search tree.  ...  In the following, we provide a simple, practical, and generally applicable method to speed up FPT algorithms.  ... 
doi:10.1016/s0020-0190(00)00004-1 fatcat:5k5gyh524ncw5dswpk3lsuykju

Novel local learning rule for neural adaptation fits Hopfield memory networks efficiently and optimally

Chris Hillar, Jascha Sohl-Dickstein, Kilian Koepsell
2013 BMC Neuroscience  
We present an algorithm to store binary memories in a Little-Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models.  ...  For memories without noise, our algorithm provably achieves optimal pattern storage and outperforms classical methods both in speed and memory recovery.  ...  We present an algorithm to store binary memories in a Little-Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models.  ... 
doi:10.1186/1471-2202-14-s1-p215 pmcid:PMC3704313 fatcat:3kyrldrxlrcstpxomub6tt6o3y

A Novel Gibbs Maximum a Posteriori (GMAP) Approach on Bayesian Nonlinear Mixed-Effects Population Pharmacokinetics (PK) Models

Seongho Kim, Stephen D. Hall, Lang Li
2009 Journal of Biopharmaceutical Statistics  
In this paper, various Bayesian Monte Carlo Markov Chain (MCMC) methods and the proposed algorithm, Gibbs maximum a posteriori (GMAP) algorithm, are compared for implementing the nonlinear mixed-effects  ...  At the mean time, data augmentation (DA) methods are used for the Random-walk Metropolis method.  ...  If a parameter has a closed form to its posterior distribution, it is categorized into a tractable parameter, and, if not, it is intractable.  ... 
doi:10.1080/10543400902964159 pmid:20183435 pmcid:PMC2829744 fatcat:glkjpix6gzbmlip6hei2i2744i

Unsupervised learning for MRFs on bipartite graphs

Boris Flach, Tomas Sixta
2013 Procedings of the British Machine Vision Conference 2013  
Persistent Contrastive Divergence) there is an alternative learning approach -a modified EM algorithm which is tractable because of the bipartiteness of the model graph.  ...  We consider unsupervised (parameter) learning for general Markov random fields on bipartite graphs. This model class includes Restricted Boltzmann Machines.  ...  To speed up learning, we used the "naive Bayes"-initialisation (see sec. 3.2). Fig. 4 shows the learning curves for the modified EM-algorithm and the stochastic gradient algorithm.  ... 
doi:10.5244/c.27.72 dblp:conf/bmvc/FlachS13 fatcat:iaheg3sclzbbfkrh46nahldneu

Tractable Variational Structures for Approximating Graphical Models

David Barber, Wim Wiegerinck
1998 Neural Information Processing Systems  
Within the variational framework for approximating these models, we present two classes of distributions, decimatable Boltzmann Machines and Tractable Belief Networks that go beyond the standard factorized  ...  Simulation results on a small benchmark problem suggest using these richer approximations compares favorably against others previously reported in the literature.  ...  The deterministic BM algorithm [6] , a variational procedure using a factorized approximating distribution, speeds up the learning of BMs, although the simplicity of this approximation can lead to undesirable  ... 
dblp:conf/nips/BarberW98 fatcat:kbrdfuqoqbczth7bh3m4nszv3y

Stochastic simulation platform for visualization and estimation of transcriptional kinetics [article]

Gennady Gorin, Mengyu Wang, Ido Golding, Heng Xu
2019 bioRxiv   pre-print
Our model includes two-state gene regulation, RNA synthesis initiation and stepwise elongation, release to the cytoplasm, and stepwise degradation, a granular description currently tractable only by simulation  ...  To facilitate comparison with experimental data, the algorithm predicts fluorescent probe signals measurable by single-cell RNA imaging.  ...  To speed up convergence to consistent parameter sets, our heuristic method uses a variable objective function, with five distinct stages that use different error metrics.  ... 
doi:10.1101/825869 fatcat:5kjczrjkdrafjplxqtmk2pzbhe

Recent Advances in Practical Data Reduction [article]

Faisal Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems.  ...  This has resulted in an algorithmic toolbox that is by now well-established. However, these theoretical algorithmic ideas have received very little attention from the practical perspective.  ...  This speeds up local search significantly. Parallelization. A general technique to speed up algorithms is parallelization.  ... 
arXiv:2012.12594v3 fatcat:vpsucno5cvgotovfiihkyyytba

The Tractable Cognition Thesis

Iris van Rooij
2008 Cognitive Science  
An argument is made to replace the P-Cognition thesis by the FPT-Cognition thesis as an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixed-parameter tractable).  ...  To utilize this constraint, a precise and workable definition of "computational tractability" is needed.  ...  Parts of this article also appeared in a doctoral dissertation submitted for a Ph.D. degree in psychology at the University of Victoria.  ... 
doi:10.1080/03640210801897856 pmid:21585437 fatcat:wjj2fslubjflrae3cukzpkoq4i

Fixed-parameter complexity and cryptography [chapter]

Michael R. Fellows, Neal Koblitz
1993 Lecture Notes in Computer Science  
We show that several parameterized problems of relevance to cryptography, including k-Subset Sum, k-Perfect Code, and k-Subset Product are likely to be intractable with respect to xed-parameter complexity  ...  We show that the problem of determining whether an n-digit number has a prime divisor less than or equal to n k can be solved in expected time f(k)n 3 by a randomized algorithm that employs elliptic curve  ...  Finding Small Factors is Randomized Fixed-Parameter Tractable In this section we describe a randomized algorithm for nding a \small" prime factor of a positive integer N that runs in expected time f(k)  ... 
doi:10.1007/3-540-56686-4_38 fatcat:ijpu4o44l5bcjgwjnd65axq44a

FAμST: Speeding up linear transforms for tractable inverse problems

Luc Le Magoarou, Remi Gribonval, Alexandre Gramfort
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
Such a desirable property can be used to speed up iterative algorithms commonly used to solve high dimensional linear inverse problems.  ...  In this paper, we propose a technique to factorize any matrix into multiple sparse factors.  ...  The principle is to adapt weights of a computational network corresponding to a fixed number of iterations of a recovery algorithm.  ... 
doi:10.1109/eusipco.2015.7362838 dblp:conf/eusipco/MagoarouGG15 fatcat:4ykusth7qjewfcomv6x6lhdlhe

An Improved Adaptive-Torque-Gain MPPT Control for Direct-Driven PMSG Wind Turbines Considering Wind Farm Turbulences

Xiaolian Zhang, Can Huang, Sipeng Hao, Fan Chen, Jingjing Zhai
2016 Energies  
It is found out that the conventional MPPT method ignores the effect of wind turbine inertia and wind speed fluctuations, which lowers WECS efficiency.  ...  Maximum power point tracking (MPPT) plays an important role in increasing the efficiency of a wind energy conversion system (WECS).  ...  In general, the TSR control regulates the generator rotor speed ω to maintain the optimal TSR and extract the maximum power.  ... 
doi:10.3390/en9110977 fatcat:jdzyxxbdanfdtaautdln355iwy

Fixed-Parameter Algorithms for Graph-Modeled Data Clustering [chapter]

Falk Hüffner, Rolf Niedermeier, Sebastian Wernicke
2009 Clustering Challenges in Biological Networks  
Fixed-parameter algorithms can efficiently find optimal solutions to some NP-hard problems, including several problems that arise in graphmodeled data clustering.  ...  This survey provides a primer about practical techniques to develop such algorithms; in particular, we discuss the design of kernelizations (data reductions with provable performance guarantees) and depth-bounded  ...  Practical Guidelines The following list sums up the experiences of our and other research groups who have implemented fixed-parameter algorithms: Fixed-Parameter Tractability in General (1) Do not despair  ... 
doi:10.1142/9789812771667_0001 fatcat:yv2okjnvjfblhlgit7cnawid4e

Page 8123 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
general method to speed up fixed-parameter-tractable algorithms.  ...  Summary: “A fixed-parameter-tractable algorithm, or FPT algo- rithm for short, gets an instance (/,k) as its input and has to decide whether (/,k) € & for some parameterized problem 7.  ... 

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics [chapter]

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 Lecture Notes in Computer Science  
We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual  ...  In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain  ...  We are grateful to Till Fluschnik and Vincent Froese for feedback to our manuscript.  ... 
doi:10.1007/978-3-662-53174-7_1 fatcat:kegsdk75mncyhjecqz3ztmtffa

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics [article]

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 arXiv   pre-print
We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual  ...  In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain  ...  We are grateful to Till Fluschnik and Vincent Froese for feedback to our manuscript.  ... 
arXiv:1606.03268v1 fatcat:6ucc6vh32rfajofrbdsxtcpznq
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