We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibilit...

In project scheduling, many problems can arise when resource fluctuations are beyond acceptable limits. To overcome this, mathematical techniques have been developed for leveling resources. However, these produce a hard and inflexible approach in scheduling projects. The authors propose a simple resource leveling approach that can be used in scheduling projects with multi-mode execution activit...

The problem of searching for a mobile robber in a simple polygon by a number of searchlights is considered. A searchlight is a stationary point which emits a single ray that cannot penetrate the boundary of the polygon. The direction of the ray can be changed continuously, and a point is detected by a searchlight at a given time if and only if it is on the ray. A robber is a point that can move...

We consider the problem of finding a minimalistic configuration of sensors that enable a simple robot inside an initially unknown polygon P on n vertices to reconstruct the visibility graph of P . The robot can sense features of its environment through its sensors, and it is allowed to move from vertex to vertex. We aim at understanding which sensorial capabilities are sufficient for the recons...

In this paper, we are concerned with computing and maintaining the exact visibility polygon V (q) of a moving point observer q in planar scenes represented by a polygon with holes with complexity of n. We propose an algorithm that applies and computes each change to V (q) in constant time as q moves to a new neighboring position. In fact, in our method changes to V (q), as the observer q moves,...

the islamic calendar is based on lunar months, which begin when the thin crescent moon is actually sighted in the western sky after sunset within a day or so after the new moon. the islamic dates begin at sunset on the previous day. the visibility of the lunar crescent as a function of the moon's age - the time counted from the new moon - is obviously of great importance to muslims. the da...