Geodesic
The pricing problem. Part~2. The computational complexity
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 6, pp. 56-71.

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For the problem, it is shown that it belongs to the class Log-APX, cannot be approximable with an absolute error limited by a constant, and the corresponding evaluation problem is non-trivial in the class $\Delta^p_2$. Also, two polynomial solvable cases of the problem are provided. Bibliogr. 8.
Keywords: computational complexity, approximability, the bilevel pricing problem, approximate algorithm, approximability class, NP-hard in the strong sense, polynomial hierarchy. 
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A. V. Plyasunov; A. A. Panin. The pricing problem. Part~2. The computational complexity. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 6, pp. 56-71. http://geodesic.mathdoc.fr/item/DA_2012_19_6_a5/

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