Searching for a Mobile Intruder in a Corridor - The Open Edge Variant of the Polygon Search Problem

Abstract

The polygon search problem is the problem of searching for mobile intruders in a simple polygon by a single mobile searcher having various degrees of visibility. This paper considers the "open edge" variant of the problem in which the given polygon P must be searched without allowing undetected intruders to reach a given edge u, under an additional assumption that any number of intruders can leave and enter P through another edge v at any time. One may view P as representing a corridor with two open exits u and v, and the task of the searcher is to force all the intruders out of P through v (but not u). We present a simple necessary condition for a polygon to be searchable in this manner by the searcher having a light bulb, and then show that the same condition is sufficient for the polygon to be searchable by the searcher having two flashlights. The time complexity of generating a search schedule is also discussed.

A Unified Framework for Two-guard Walk Problem

“…3, if we select vertex 4 as the entrance s and vertex 13 as the exit g, as shown in Fig. 21 (a), then VT P (4,13) is the corresponding visibility rectangle imposed on VD P , as shown in Fig. 21 (b).…”

“…Bhattacharya et al [2] come up with an optimal algorithm for the same problem. In [4], Crass et al study an ∞-searcher in an open-edge "corridor", which uses edges as the entrance and exit. An ∞-searcher has a visibility of 360 o [14].…”

Visibility-Based Pursuit-Evasion in an Unknown Planar Environment

“…A complete algorithm for the case of omnidirectional visibility was first presented in LaValle et al (1997). Solutions to the case in which the pursuer has one or more detection beams, or in which several pursuers are present, are considered in Crass, Suzuki, and Yamashita (1995), Lee, Shin, and Chwa (1999), Simov, Slutzki, and LaValle (2000), Suzuki et al (2001) and Umemoto et al (1998), for various types of polygons. A pursuit-evasion algorithm for curved environments was presented in LaValle and Hinrichsen (2001).…”