On computational complexity of construction of c -optimal linear regression models over finite experimental domains
By: Jaromír Antoch, Michal Černý and Milan Hladík
Open Access
|Nov 2012References
- [1] ARORA, S.-BARAK, B.: Computational Complexity. A Modern Approach. Cambridge University Press, Cambridge, 2009.
- [2] ATKINSON, A.-DONEV, A.-TOBIAS, R.: Optimum Experimental Designs with SAS. Oxford University Press, Oxford, 2007.
- [3] ˇC ERN´Y, M.-HLAD´IK, M.: Two complexity results on c-optimality in experimental design, Computational Optimization and Applications 51 2012, 1397-1408, http://www.springerlink.com/content/115ttx6lu150434k/fulltext.pdf
- [4] ˇC ERN´Y, M.-HLAD´IK, M.-SKOˇCDOPOLOV´A, V.: On computationally complex in- stances of the c-optimal experimental design problem: Breaking RSA-based cryptography via c-optimal designs, in: Proc. of 19th Internat. Conference on Comput. Statist.- -CompStat ’10 (Y. Lechevallier, G. Saporta, eds.), Paris, France, Physica Verlag, Heidel- berg, 2010, pp. 879-886.
- [5] EDMONDS, J.: Systems of distinct representatives and linear algebra, J. Res. Natl. Bur. Stand., Sec. B 71B (1967), 241-245.
- [6] GREENLAW, R.-HOOVER, H.-RUZZO, W.: Limits to Parallel Computation. P-completeness Theory. Oxford University Press, Oxford, 1995.
- [7] HARMAN, R.-JUR´IK, T.: Computing c-optimal experimental designs using the simplex method of linear programming, Comput. Statist. Data Anal. 53 (2008), 247-254.
- [8] KHACHIYAN, L.: A polynomial algorithm for linear programming, Dokl. Akad. Nauk SSSR 244 (1979), No. 5, 1093-1096.
- [9] KLEE, V.-MINTY, G. J.: How good is the simplex algorithm? Inequalities III, in: Proc. of the 3rd Symposium on Inequalities held at the University of California, Los Angeles, Calif., 1969 (O. Shisha, ed.), Academic Press, New York, 1972, pp. 159-175.
- [10] ODIFREDDI, P.: Classical Recursion Theory. Volume I. Stud. Logic Found. Math., Vol. 125, Elsevier, Amsterdam, 1999.
- [11] PAPADIMITRIOU, C.: Computational Complexity. Addison-Wesley, Longman, 1995.
- [12] P´AZMAN, A.: Foundations of Optimum Experimental Design. Reidel Publ. Comp., Dordrecht, 1986.
- [13] PUKELSHEIM, F.-RIEDER, S.: Efficient rounding in approximate designs, Biometrika 79 (1992), 763-770.
- [14] RAO, C. R.: Linear Statistical Inference and its Applications. John Wiley & Sons, New York, 1973.
- [15] ROOS, C.-TERLAKY, T.-VIAL, J.-P.: Interior Point Methods for Linear Optimization . Springer, Heidelberg, 2006.
- [16] SCHRIJVER, A.: Theory of Linear and Integer Programming. John Wiley & Sons, New York, 2000.
- [17] WHITTLE, P.: Some general points in the theory of optimal experimental design, J. Roy. Statist. Soc. Ser. B. 35 (1973), 123-130.
DOI: https://doi.org/10.2478/v10127-012-0002-3 | Journal eISSN: 1338-9750 (formerly 1210-3195) | Journal ISSN: 1210-3195
Language: English
Page range: 11 - 21
Published on: Nov 13, 2012
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2012 Jaromír Antoch, Michal Černý, Milan Hladík, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.