Abstract
The problems degree-limited graph of nodes considering the weight of the vertex or weight of the edges, with the aim to find the optimal weighted graph in terms of certain restrictions on the degree of the vertices in the subgraph. This class of combinatorial problems was extensively studied because of the implementation and application in network design, connection of networks and routing algorithms. It is likely that solution of MDBCS problem will find its place and application in these areas. The paper is given an ILP model to solve the problem MDBCS, as well as the genetic algorithm, which calculates a good enough solution for the input graph with a greater number of nodes. An important feature of the heuristic algorithms is that can approximate, but still good enough to solve the problems of exponential complexity. However, it should solve the problem heuristic algorithms may not lead to a satisfactory solution, and that for some of the problems, heuristic algorithms give relatively poor results. This is particularly true of problems for which no exact polynomial algorithm complexity. Also, heuristic algorithms are not the same, because some parts of heuristic algorithms differ depending on the situation and problems in which they are used. These parts are usually the objective function (transformation), and their definition significantly affects the efficiency of the algorithm. By mode of action, genetic algorithms are among the methods directed random search space solutions are looking for a global optimum.
Highlights
General problems of degree-constraind graphs, consider the nodes of weight or weight on the vertices, where the goal is to find the optimal weighted graph, with set limits for levels of subgraph nodes
In the Theory of complexity, NP is a set of decision problems that can be solved by nondeterministic Turing machine
The importance of this class of decision problems is that it contains many interesting problems of search and optimization, where we want to determine whether there is some solution to the problem, but whether this is the optimal solution
Summary
General problems of degree-constraind graphs, consider the nodes of weight or weight on the vertices, where the goal is to find the optimal weighted graph, with set limits for levels of subgraph nodes. This class of combinatorial problems has been extensively studied for use in designing networks. And is a spanning tree for the subgraph , ILP formulation of the model for finding the maximum degree of a connected subgraph constraints is given below, part of the paper [4]. Theorem 1. [4] The MDBCS problem can be solved if and only if the following conditions (2) - (7) holds or their equivalent set of conditions
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