2007 Fiscal Year Final Research Report Summary
A study on the algorithms for searching a static or moving target in a polygonal region
| Project/Area Number |
17500011
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Tokai University |
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Principal Investigator |
TAN Xuehou Tokai University, School of High-technology for Human Welfare, Professor (50256179)
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| Project Period (FY) |
2005 – 2007
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| Keywords | algorithms / computational geometry / watchman route problem / polygon search problem / on-line algorithms / competitive factor / chain guards / complexity |
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| Research Abstract |
We presented a new, on-line strategy for a mobile robot to explore an unknown polygon P. starting at a boundary point, which outputs a so-called watchman mute such that every interior point of P is visible from at least one point along the route. The length of the robot's route is guranteed to be at roost 6.7 times that of the shortest watchman route that cnuld be computed off-line. This gives a significant improvement-upon the previously known 26.5-competitive strategy.
For the polygon search problem, we also developed an efficient algorithm. Given a simple polygon P with two vertices u and v, the three-guard problem asks whether three guards can move from u to v such that the first and third guards are separately on two boundary chains of P from u to v, and the second guard is always kept to be visible from two other guards inside P. We can decide whether there exists a solution fir the three-guard problem in O(n log n) time, and ifso, generate a walk in O(n log n+in) time, where n denotes the number of vertices of P and m(≦(n^2)) the size of the optimal walk. This improves upon the previous time bounds O(n^2) and O(n^2 log n), respectively.
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Research Products
(8 results)
