• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.2
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• pp.369-374
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• 2010

The shortest path between two points inside a simple polygon P is a minimum-length path among all paths connecting them which don't pass by the exterior of P. A linear time algorithm for computing the shortest path in a general simple polygon requires triangulating a polygon as preprocessing. The linear time triangulating is known to very complex to understand and implement it. It is also inefficient in case that the input without very large size is given because its time complexity has a big constant factor. In this paper, we present the customized shortest path algorithm for a segment-visible polygon which is a simple polygon weakly visible from an internal line segment. Our algorithm doesn't require triangulating as preprocessing and consists of simple procedures such as construction of convex hulls, so it is easy to implement and runs very fast in linear time.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.11
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• pp.1437-1445
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• 1999

n개의 꼭지점을 가진 단조(monotone) 다각형은 2차원 평면상의 임의의 선분에 단조 적인 2개의 체인으로 구성된다. 단조 다각형의 내부를 경로 상에서 모두 감시할 수 있는 최소 링크를 가진 경비원 경로(watchman route with minimum links)는 최소 개수의 선분으로 구성된 경로로서 하나 이상 존재할 수 있다. 본 논문에서는 단조 다각형의 최소 링크를 가진 경비원 경로들 중에서 최단 경비원 경로를 구하는 O(n) 시간의 알고리즘을 제시한다.Abstract A monotone polygon consists of n vertices and is a union of two monotone chains with respect to some line segment in the plane. A watchman route with minimum-links is a polygonal path such that each point in the interior of the polygon can be visible from at least one point along the route. There may be more than one watchman route with minimum links for given monotone polygon. In this paper, we present an algorithm with O(n) time that finds a shortest watchman route among the watchman routes with minimum links in a monotone polygon.