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Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
| Venue: | SIAM JOURNAL ON COMPUTING |
| Citations: | 155 - 3 self |
BibTeX
@ARTICLE{Yamashita_searchingfor,
author = {Masafumi Yamashita and Hideki Umemoto and Ichiro Suzuki and Tsunehiko Kameda},
title = {Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers},
journal = {SIAM JOURNAL ON COMPUTING},
year = {},
volume = {21},
pages = {863--888}
}
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Abstract
The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant is limited to the points on the ray. The intruders can move continuously with unbounded speed. We denote by ps(P ) the polygon search number of a simple polygon P , which is the number of searchers necessary and sufficient to search P . Let n, r, b and g be the number of edges, the number of reflex vertices, the bushiness, and the size of a minimum guard set of P , respectively. In this paper, we present matching upper and (worst case) lower bounds of 1 + blog 3 (2b + 1)c on ps(P ). Also upper bounds on ps(P ) in terms of n; r and g are presented; ps(P ) 1 + blog 3 (n \Gamma 3)c; ps(P ) 1 + blog 3 rc, and ps(P ) 2 + dlog 2 ge. These upper bounds are tight or almost tight in the worst case, since we show that for any natural number s 2, there is a polygon P such that ps(P ) = log 3 (n + 1) = log 3 (2r + 3) = 1 + log 3 (2g \Gamma 1) = s.
