Barrier coverage

A region is a belt if its boundary consists of two parts such that every point in one part has equal distance to the other part. This distance is called width and these two parallel boundary parts are called two banks. (When a belt is considered as river, two boundary parts are two banks.) For example, ring and strip are belts. A belt is closed if it is a closed and bounded region, such as ring. An open belt can be seen as a piece of a closed belt between two parallel lines (Fig. 10.1). In such a case, the boundary on the two lines are considered to be open and called belt-ends. Hence, an open belt keeps its boundary consisting of two banks and two belt-ends. For simplicity, from now on, by a belt, we mean an open belt since the closed belt can be turned to an open belt easily. In fact, use a line to cut a closed belt. Then the closed belt can be turned to an open belt and what we do for an open belt can be extended to a closed belt without any trouble.