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Approximation schemes for a class of subset selection problems

Kirk Pruhs, Gerhard J. Woeginger
2007 Theoretical Computer Science  
In this paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems.  ...  The approximability status of this problem has been open for some time.  ...  The class of subset selection problems described in Definition 1.1 is very general, and it contains many problems with very bad approximability behavior.  ... 
doi:10.1016/j.tcs.2007.03.006 fatcat:ozd7bpnilnhgdnksaygmm5ywle

Constructing the highest degree subgraph for dense graphs is in N b A S

Alexander E. Andreev, Andrea E.F. Clementi, JoséD.P. Rolim
1996 Theoretical Computer Science  
We then provide an .N'V-approximation scheme computing approximate solutions for dense graphs, thus proving that, in this case, the problem belongs to the A'%&9' class.  ...  This hardness result gives a clear motivation in studying the approximability of the Highest Degree Problem even for this restricted case.  ...  Acknowledgements We would like to thank Maria Serna for helpful ideas.  ... 
doi:10.1016/0304-3975(96)00014-x fatcat:zcd5zgse7zglnkyuienk7zg3mu

Identification of Full and Partial Class Relevant Genes

Zexuan Zhu, Yew-Soon Ong, Jacek M Zurada
2010 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
Using multiclass cancer feature selection approaches, it is now possible to identify genes relevant to a set of cancer types.  ...  Subsequently, a Markov blanket embedded memetic algorithm is proposed for the simultaneous identification of both FCR and PCR genes.  ...  ACKNOWLEDGMENTS This work was funded in part under the A*STAR SERC Grant 052 015 0024 administered through the National Grid Office.  ... 
doi:10.1109/tcbb.2008.105 pmid:20431146 fatcat:mgbv54uylrgvfosl6vykbbs5iq

Data Subset Selection For Efficient Svm Training

Sara Mourad, Ahmed Tewfik, Haris Vikalo
2018 Zenodo  
Publication in the conference proceedings of EUSIPCO, Kos island, Greece, 2017  ...  Our scheme first performs an approximate nearest neighbor search and then employs a greedy algorithm to select the subset for SVM training.  ...  In Figure 1 , we show the results of using our algorithm to select a subset to classify '1 vs rest', and compare its performance to random selection schemes.  ... 
doi:10.5281/zenodo.1160174 fatcat:qsex46vdf5dnxmibj6h4rkefnm

Rough Set-Based Dataset Reduction Method Using Swarm Algorithm and Cluster Validation Function

Kuang-Yu Huang, Ting-Hua Chang, Shann-Bin Chang
2015 2015 48th Hawaii International Conference on System Sciences  
The performance of the proposed method is compared with that of two existing attribute reduction and classification methods for eight benchmark datasets.  ...  The results confirm that the proposed method provides an effective tool for solving simultaneous attribute reduction and discretization problems. R P m j j J J ¦ where H J H J H J H J H J J J  ...  Acknowledgements This study was financially supported by the Research Grant MOST 103-2410-H-275 -004 -from Taiwan's Ministry of Science and Technology. References  ... 
doi:10.1109/hicss.2015.180 dblp:conf/hicss/HuangCC15 fatcat:ko7xijfvnnacvp47hbolv6hlrm

Fast approximate kernel-based similarity search for image retrieval task

David Gorisse, Matthieu Cord, Frederic Precioso, Sylvie Philipp-Foliguet
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
We introduce a method for fast approximate similarity search in large image databases with our kernel-based similarity metric.  ...  In content based image retrieval, the success of any distance-based indexing scheme depends critically on the quality of the chosen distance metric.  ...  Acknowledgment The authors are grateful to A. Andoni for providing the package E 2 LSH.  ... 
doi:10.1109/icpr.2008.4761225 dblp:conf/icpr/GorisseCPP08 fatcat:45k2glq6jbhepoe67bjxjit26u

A Theory and Algorithms for Combinatorial Reoptimization

Baruch Schieber, Hadas Shachnai, Gal Tamir, Tami Tamir
2017 Algorithmica  
This includes fully polynomial time reapproximation schemes for DP-benevolent problems, a class introduced by Woeginger (Proc.  ...  Thus, we distinguish here for the first time between classes of reoptimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for  ...  Acknowledgments: We thank Baruch Schieber and Rohit Khandekar for helpful discussions.  ... 
doi:10.1007/s00453-017-0274-8 fatcat:arlnvrogqfeitk7qcnnvreqsyu

A Theory and Algorithms for Combinatorial Reoptimization [chapter]

Hadas Shachnai, Gal Tamir, Tami Tamir
2012 Lecture Notes in Computer Science  
This includes fully polynomial time reapproximation schemes for DP-benevolent problems, a class introduced by Woeginger (Proc.  ...  Thus, we distinguish here for the first time between classes of reoptimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for  ...  Acknowledgments: We thank Baruch Schieber and Rohit Khandekar for helpful discussions.  ... 
doi:10.1007/978-3-642-29344-3_52 fatcat:kdxjjczlpza5hckefb4ubju3yq

Adaptive Aspects of Combining Approximation Spaces [chapter]

Jakub Wróblewski
2004 Rough-Neural Computing  
A notion of parameterized approximation space is used to model a process of the classifier construction.  ...  The paper addresses issues concerning a problem of constructing optimal classification algorithm.  ...  Acknowledgements This work was supported by the grant of Polish National Committee for Scientific Research (KBN) No. 8T11C02519.  ... 
doi:10.1007/978-3-642-18859-6_6 fatcat:azyhqyi5bzaf3nbu2adhzkn7oq

Complexity of Solutions Combination for the Three-Index Axial Assignment Problem

Lev G. Afraimovich, Maxim D. Emelin
2022 Mathematics  
Such combination can be applied in a wide range of heuristic and approximate algorithms for solving the assignment problem, instead of the commonly used strategy of selecting the best solution among the  ...  In this work we consider the NP-hard three-index axial assignment problem. We formulate and investigate a problem of combining feasible solutions.  ...  Acknowledgments: The authors would like to thank anonymous reviewers for their suggestions and comments. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math10071062 fatcat:ll6azy6jczhmzprfioguilqiei

Information criteria performance for feature selection

Mohamed Abadi, Olivier Alata, Christian Olivier, Majdi Khoudeir, Enguerran Grandchamp
2011 2011 4th International Congress on Image and Signal Processing  
Results show stability and convergence properties of this tool and its ability to select representative subsets (in the sense that the subset of feature is a good characterization of the classes in which  ...  This paper shows the information criteria (IC) performances in feature selection framework. Feature selection aims to select a representative subset among a wide set of features.  ...  ACKNOWLEDGMENT The authors want to thanks the European institutions and more precisely the INTERREG IV program within the CESAR Part II project leads by the University of Antilles and Guyana and the Poitou-Charentes  ... 
doi:10.1109/cisp.2011.6100275 fatcat:fjyugikfxfhdhccc62st7mowtq

The Problem of Convergence of Classifiers Construction Procedure in the Schemes of Logical and Algorithmic Classification Trees

Igor Povkhan, Oksana Mulesa, Olena Melnyk, Yuriy Bilak, Volodymyr Polishchuk
2022 Computer Modeling and Intelligent Systems  
It suggests the upper evaluation of complexity for the scheme of algorithms tree in the problem of approximation of real data array by a set of generalized features with a fixed criterion of termination  ...  The paper considers the problem of convergence in the procedure of classifier schemes synthesis by methods of logical and algorithmic classification trees.  ...  state registration number of the work is 0106V00285, the category of work is fundamental research (ID-2201020), 01 -Fundamental research on the most important problems of natural, social and humanitarian  ... 
doi:10.32782/cmis/3137-1 fatcat:sruf5vhkmvfw7av67mlek5fhgm

There is no EPTAS for two-dimensional knapsack

Ariel Kulik, Hadas Shachnai
2010 Information Processing Letters  
The goal is to select a subset of the items of maximum total profit such that the sum of all vectors is bounded by the bin capacity in each dimension.  ...  Furthermore, we show that unless all problems in SNP are solvable in sub-exponential time, there is no approximation scheme for two-dimensional knapsack whose running time is f (1/ε)|I| o( √ 1/ε) , for  ...  A maximization problem Π admits a polynomial-time approximation scheme (PTAS) if there is an algorithm A(I, ε) such that, for any ε > 0 and any instance I of Π, A(I, ε) outputs a (1 − ε)-approximate solution  ... 
doi:10.1016/j.ipl.2010.05.031 fatcat:i5lhqvgr4jhqfinwy7xmu2sze4

Supervised learning through the lens of compression

Ofir David, Shay Moran, Amir Yehudayoff
2016 Neural Information Processing Systems  
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification.  ...  We then consider Vapnik's general learning setting: we show that in order to extend the compressibility-learnability equivalence to this case, it is necessary to consider an approximate variant of compression  ...  A selection scheme is a pair (κ, ρ) of maps for which the following holds: • κ is called the selection map.  ... 
dblp:conf/nips/DavidMY16 fatcat:brswuvsh2jhonfbfho27rem3rm

A Hypergraph-Based Approach to Feature Selection [chapter]

Zhihong Zhang, Edwin R. Hancock
2011 Lecture Notes in Computer Science  
The feature selection problem is essentially a combinatorial optimization problem which is computationally expensive.  ...  Experimental results demonstrate the effectiveness of our feature selection method on a number of standard data-sets.  ...  . , f m )P (c) . (6) The main reason for using I(F ; C) as a feature selection criterion is that since I(F ; C) is a measure of the reduction of uncertainty in class C due to knowledge of the feature vector  ... 
doi:10.1007/978-3-642-23672-3_28 fatcat:5da24equjvhqpk2i4ks7vuctne
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