The power transformation of Newton's binomial forms two equal 3n±1 algorithms for transformations of numbers n belongs to N, each of which have one infinite cycle with a unit lower limit of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower limits of the corresponding cycles, and the last element goes to a multiple of three odd numbers.
This paper proposes a new application of the stochastic game model to solve the problem of self- organization of the Hamiltonian cycle of a graph. To do this, at the vertices of the undirected graph are placed game agents, whose pure strategies are options for choosing one of the incident edges. A random selection of strategies by all agents forms a set of local paths that begin at each vertex of the graph. Current player payments are defined as loss functions that depend on the strategies of neighboring players that control adjacent vertices of the graph.
The article deals with the modeling of the repair of the roads of the territorial community in the presence of funds and depending on the state of roads. To simulate the proposed search method using the minimum spanning tree algorithm based on modified Prima. Examples of the use of the proposed approach within the framework of the Khodoriv territorial communities are presented.
Possibilities of modelling optimization design problems as the extreme combinatorial graph problems and solving them in MS Excel Solver are studied. Drawbacks of existing models from considering their realization in MS Excel Solver are analyzed.
The article deals with reasons why the planned network resource is not used completely. The main attention is paid to the dynamic routing protocol, which does not consider the current load of local network segments according to the principle of its functioning. In the paper local segments loading considers with existence of a constant flow to reduce the computational complexity of the proposed method. The method is proposed in the work to maximize the use of network resources and resource allocation improving based on alternative routes variation through less loaded local segment.
The paper proposes a method, algorithms and its implementations using dominance rules for minimizing the total tardiness on a single machine based on shortest Hamiltonian path in a arbitrary graph that improve the efficiency and not reduce the execution time. Metrics for evaluating the effectiveness of the dominance rules are proposed. The experimental results of algorithms are developed that justify the effectiveness of the proposed modifications by getting local optimal solutions during procedure.