Optimal Ordering of Conflicting Objects and the Traveling Salesman Problem

• Published in: Труды Института системного программирования РАН
• Main Authors: Alexey Voevodin, Semen Kosyachenko
• Format: Article
• Language: English
• Published: Russian Academy of Sciences, Ivannikov Institute for System Programming 2018-10-01
• Subjects: оптимальное размещение; задача коммивояжера; tsp; np-трудные задачи; ленточные матрицы; разреженные матрицы; жадный алгоритм; штрафная функция; конфликты, сети сми
• Online Access: https://ispranproceedings.elpub.ru/jour/article/view/881
• ISSN: 2079-8156; 2220-6426

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.