Computational Optimization and Applications

, Volume 51, Issue 3, pp 1397–1408 | Cite as

Two complexity results on c-optimality in experimental design

  • Michal Černý
  • Milan Hladík


Finding a c-optimal design of a regression model is a basic optimization problem in statistics. We study the computational complexity of the problem in the case of a finite experimental domain. We formulate a decision version of the problem and prove its \(\boldsymbol{\mathit{NP}}\)-completeness. We provide examples of computationally complex instances of the design problem, motivated by cryptography. The problem, being \(\boldsymbol{\mathit{NP}}\)-complete, is then relaxed; we prove that a decision version of the relaxation, called approximate c-optimality, is P-complete. We derive an equivalence theorem for linear programming: we show that the relaxed c-optimality is equivalent (in the sense of many-one LOGSPACE-reducibility) to general linear programming.


Linear programming Optimal design NP-completeness P-completeness 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of EconometricsUniversity of Economics, PraguePragueCzech Republic
  2. 2.Faculty of Mathematics and Physics, Department of Applied MathematicsCharles University, PraguePragueCzech Republic

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