Optimal Ordering of Conflicting Objects and the Traveling Salesman Problem
The paper presents the setting of the problem of optimal ordering of conflicting objects related to the Travelling Salesman Problem (TSP). The problem of optimal ordering of conflicting objects appears in sociology, in graph analysis and finding in them optimal paths, in advertising in various media. Solution algorithms are described for this and related problems. The TSP with sparse matrix is also considered. For sparse practice cases of the TSP necessary and sufficient conditions are proved to objective function attained its minimum and the algorithms guaranteeing exact solution are constructed. The practical results of analytical and numerical investigations of algorithm complexity and solution accuracy are presented as well as recommendations for the algorithm applications to the solution of these problems.