### 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 vision 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 + [log_{3}(2b + 1)J on ps(P). Also upper bounds on ps(P) in terms of n, r, and g are presented; ps(P) ≤ 1 + Log_{3}(n - 3)J, ps(P) ≤ 1 + [Log_{3} r], and ps(P) ≤ 2 + [log_{2} g]. 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 - 1) = s.

Original language | English |
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Pages (from-to) | 208-236 |

Number of pages | 29 |

Journal | Algorithmica (New York) |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2001 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

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## Cite this

*Algorithmica (New York)*,

*31*(2), 208-236. https://doi.org/10.1007/s00453-001-0045-3