Abstract
In this paper, we show that the problem under study is in the class Log-APX, cannot be approximate with absolute error bounded by a constant, and the associated evaluation problem is nontrivial in the class Δ p2 . The two cases of the problem solvable in polynomial time are provided.
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A.V. Plyasunov and A. A. Panin, “The Pricing Problem.Part I: Exact and Approximate Algorithms,” Diskretn. Anal. Issled. Oper. 19(5), 83–100 (2012) [J. Appl. Indust. Math. 7 (1), 241–251 (2013)].
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York, 1979; Mir, Moscow, 1982).
A. Schrijver, Theory of Linear and Integer Programming (Wiley, Chichester, 1986; Mir, Moscow, 1991).
M. Attallah, Algorithms and Theory of Computation Handbook (CRC Press LLC, Boca Raton, 1999).
G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties (Springer, Berlin, 1999).
S. J. Dempe, Foundations of Bilevel Programming (Kluwer Acad. Publ., Dordrecht, 2002).
P. Hanjoul, P. Hansen, D. Peeters, and J.-F. Thisse, “Incapacitated Plant Location under Alternative Spatial Price Policies,” Management Sci. 36, 41–57 (1990).
E. W. Leggette, Jr., and D. J. Moore, ” “Optimization Problems and the Polynomial Hierarchy,” Theoret. Comput. Sci. 15(3), 279–289 (1981).
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Original Russian Text © A.V. Plyasunov, A.A. Panin, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 6, pp. 56–71.
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Plyasunov, A.V., Panin, A.A. The pricing problem. Part II: Computational complexity. J. Appl. Ind. Math. 7, 420–430 (2013). https://doi.org/10.1134/S1990478913030150
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DOI: https://doi.org/10.1134/S1990478913030150