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Doklady Mathematics - In this paper, for the first time, we provide a quasi-polynomial time approximation scheme for the well-known capacitated vehicle routing problem formulated in metric spaces... 相似文献
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Journal of Global Optimization - The capacitated vehicle routing problem (CVRP) is the well-known combinatorial optimization problem having numerous practically important applications. CVRP is... 相似文献
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Journal of Global Optimization - 相似文献
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O. Yu. Khachay 《Differential Equations》2011,47(4):604-607
We consider the Cauchy problem for two nonlinear differential equations with a small parameter multiplying the derivative
in one of the equations. The right-hand side of this equation has a zero of high order at the origin with respect to one of
the unknown functions. We construct and justify a uniform asymptotic approximation to the solution with accuracy of any power
of the small parameter. We reveal two boundary layers in a neighborhood of the initial point. 相似文献
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Vl. D. Mazurov M. Yu. Khachay M. I. Poberii 《Proceedings of the Steklov Institute of Mathematics》2008,263(2):93-107
In the paper, the computational and approximational complexity of the minimal affine separating committee problem, as well as of some important special cases of this problem, is investigated. 相似文献
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O. Yu. Khachay 《Differential Equations》2008,44(2):282-285
We consider the Cauchy problem for the nonlinear differential equation where ? > 0 is a small parameter, f(x, u) ∈ C ∞ ([0, d] × ?), R 0 > 0, and the following conditions are satisfied: f(x, u) = x ? u p + O(x 2 + |xu| + |u|p+1) as x, u → 0, where p ∈ ? \ {1} f(x, 0) > 0 for x > 0; f u 2(x, u) < 0 for (x, u) ∈ [0, d] × (0, + ∞); Σ 0 +∞ f u 2(x, u) du = ?∞. We construct three asymptotic expansions (external, internal, and intermediate) and prove that the matched asymptotic expansion approximates the solution uniformly on the entire interval [0, d].
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$$\varepsilon \frac{{du}}{{dx}} = f(x,u),u(0,\varepsilon ) = R_0 ,$$
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Mikhail Yu. Khachay 《Journal of Mathematical Modelling and Algorithms》2007,6(4):547-561
Two special cases of the Minimum Committee Problem are studied, the Minimum Committee Problem of Finite Sets (MCFS) and the
Minimum Committee Problem of a System of Linear Inequalities(MCLE). It is known that the first of these problems is NP-hard (see (Mazurov et al., Proc. Steklov Inst. Math., 1:67–101, 2002)). In this paper we show the NP-hardness of two integer optimization problems connected with it. In addition, we analyze the hardness of approximation to
the MCFS problem. In particular, we show that, unless NP⊂TIME(n
O(loglogn
)), for every ε>0 there are no approximation algorithms for this problem with approximation ratio (1–ε)ln (m–1), where m is the number of inclusions in the MCFS problem. To prove this bound we use the SET COVER problem, for which a similar result
is known (Feige, J. ACM, 45:634–652, 1998). We also show that the Minimum Committee of Linear Inequalities System (MCLE) problem is NP-hard as well and consider an approximation algorithm for this problem.
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