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We propose a dead-end control algorithm for the exact solution of NP-hard combinatorial optimization problems. The efficiency of the algorithm is demonstrated by examples of solving the set-partition and 0-1 knapsack problems. The paper also shows that the use of the idea of dead-end controls when implementing the dynamic programming method can considerably reduce the number of problem state variables at each optimization step. A comparative analysis of the proposed method with known algorithms for solving these problems is carried out. [ABSTRACT FROM AUTHOR]

We consider a class of hyperbolic systems of linear inhomogeneous partial differential equations with one spatial variable. As a rule, in the case of systems of partial differential equations, when solving particular problems, additional conditions are immediately used to ensure the uniqueness of the solution. However, this greatly complicates the construction of a solution in the case of additional conditions of nonstandard form. For a similar situation in the case of ordinary differential equations, one tries to find a general solution, for which one can then try to use the given additional conditions. However, for systems of partial differential equations, this approach is difficult, since, as a rule, in this case it is not possible to construct the general solution. For the class of systems of linear inhomogeneous partial differential equations considered in the present paper, it was possible to find an algorithm for constructing a general solution. A distinctive feature of the considered systems of equations is the multiplicity of the corresponding characteristics. As an application of the proposed algorithm, a general solution of the Kolmogorov system of equations for the probabilities of the states of a process is obtained, which describes the behavior of a popular model of a stochastic system of the type -out-of- with a general distribution of the repair time for failing components. The indicated system of Kolmogorov equations is a system of partial differential equations of the mentioned class. Therefore, it is possible to construct a general solution for this system. [ABSTRACT FROM AUTHOR]

This paper considers construction algorithms for the topological 2-D drawing of a graph. These algorithms allow to store, describe and modify the existing information on the drawing of a graph. Finally, we introduce necessary notions and structures to solve the problem of the topological 2-D drawing of a graph. [ABSTRACT FROM AUTHOR]

The concept of a risk-guaranteed solution for many-criteria problems under uncertainty, which is typical of emergency situations, and a solution algorithm for these problems are described in Part I of this paper. In Part II, this algorithm is realized for a two-criteria problem under bounded uncertainties and linear-quadratic criteria. [ABSTRACT FROM AUTHOR]