| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| 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.
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