A study on the algorithms for touring a sequnec of geometric objects
| Project/Area Number |
15K00023
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | Tokai University |
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Principal Investigator |
Tan Xuehou 東海大学, 情報理工学部, 教授 (50256179)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 計算幾何 / 巡回セールスマン問題 / 警備員巡回路問題 / 順序性 / 最短路問題 / 射線巡回路問題 / 多項式時間アルゴリズム / グラフの膨張因子 / アルゴリズム / データ構造 / 競合比 / オンラインアルゴリズム |
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| Outline of Final Research Achievements |
This research focusses on the development of efficient algorithms for computing a shortest route that visits a set of geometric objects, in a given or computed order. For the watchman route problem for lines and the traveling salesman problem for rays, we presented O(n exp(6)) and O(n exp(5)) time solutions respectively, improving upon the known results. For the problem of touring a sequence of convex polygons, we developed a simplified version of the so-called last step shortest path maps, which can be used to give new and efficient solutions. For the on-line watchman route and related problems, we gave new on-line strategies, whose competitive factors are far smaller than the known ones. Finally, we also presented efficient algorithms for the coppers and robbers game on a plane graph.
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| Academic Significance and Societal Importance of the Research Achievements |
研究テーマが巡回セールスマン問題や警備員巡回路問題等に関係しているため、研究成果の学術的意義が高い。本研究で考案した最短路パスマップというデータ構造は、幾何学的対象物を与えられた序列で訪れる最短の経路を求めるのに役に立つ。また、n本の射線を訪れる最短の巡回路を求める問題および関連問題に対する初めての多項式時間解法は提案することができた。これらの研究成果は計算幾何やアルゴリズム論の発展に寄与することに違いない。
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Report
(6 results)
Research Products
(15 results)
