2013 Fiscal Year Final Research Report
A graph-based approach to the visibility-based pursuit-evasion problem
| Project/Area Number |
23500024
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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 |
Fundamental 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) |
2011 – 2013
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| Keywords | アルゴリズム / 計算幾何 / 幾何学的捜索問題 / 可視性 / ツーガイド問題 / LR-可視的多角形 |
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| Research Abstract |
This work presents a new method for solving the visibility-based pursuit-evasion problems, mainly by transforming them into the shortest path problems in graphs. For the two-guards problem, we presented the O(n^2) time algorithms for computing the search schedules in which the sum of the distances traveled by the two guards is minimized, or the maximum distance between the two guards is minimized. For the problem of searching mobile intruders in a circular corridor by two 1-searchers, we gave an O(n*n) time solution. For the problem of finding a simple path that turns at the points from the given n points but avoids the boundary of the given polygon of m vertices, we presented an O((n*n+m) log m) time algorithm, which greatly improves upon the previous O((n m)*(n m)) time bound. Finally, we also gave a simple characterization of LR-visibility polygons and a linear-time algorithm for determining whether a given polygon is LR-visible.
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