A human observer can effortlessly identify visible portions of geometric objects present in the
environment. However, computations of visible portions of objects from a viewpoint involving …

Given a simple polygon P of n vertices, the watchman route problem asks for a shortest
(closed) route inside P such that each point in the interior of P can be seen from at least one …

This thesis investigates several problems related to searching a polygonal area for intruders.
The mutual visibility between an arbitrary pair of points on the boundary of a polygon is an …

A room is a simple polygon with a prespecified point, called the door, on its boundary. A
search starts at the door and must detect any intruder that may be in the room, while making …

We study the problem of searching for a mobile intruder in a polygonal region P with a door
d (called a room) by a mobile searcher. The objective is to decide whether there exists a …

A room is a simple polygon with a prespecified point, called the door, on its boundary.
Search starts at the door, and must detect all intruders that may be in the room, while making …

Given a simple polygon P with two vertices u and v, the three-guard problem asks whether
three guards can move from u to v such that the first and third guards are separately on two …

A polygon P is a street if there exist points (u, v) on the boundary such that P is weakly
visible from any path from u to v. Optimal strategies have been found for on-line searching of …

We consider the problem of searching for a mobile intruder in a circular corridor by two
mobile searchers, who hold one flashlight. A circular corridor is a polygon with one …

A room is a simple polygon with a prespecified point, called the door, on its boundary.
Search may be conducted by two guards on the boundary who keep mutual visibility at all …