Special cases of several routing problems and various relaxations of routes

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540140
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: ODA YOSHIAKI 慶應義塾大学, 理工学部, 准教授 (90325043)
• Research Collaborator: WATANABE MAMORU
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 組合せ論 / 離散数学 / 経路問題 / 整数の分割

Outline of Final Research Achievements

The Traveling Salesman Problem is the problem to find a shortest route which starts from some city, visits each city exactly once and comes back to the initial city. This problem is one of the most famous NP-hard problems. This shows that when the number of cities increases it becomes to be hard to find a shortest route (optimal solution) in a reasonable time (polynomial time). In this work, we studied those problems from mathematical points of view and found polynomial time solvable cases for the problem and its extended routing problems. In this research area, we need not only characterizations of optimal solutions for those cases together with proofs but also algorithms to compute a shortest routes among all solutions.
Also, we worked several problems on balanced partitions for cyclic permutations, permutations and sets of finite integers which relate to the Traveling Salesman Problem.

Free Research Field

数物系科学