In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to detect certain events in networks, where the sensors have a limited ability to react under changing conditions in the network. A 1-movable dominating set is a dominating set S ⊆ V (G) such that for every v ∈ S, either S − {v} is a dominating set, or there exists a vertex u ∈ (V (G) − S) ∩ N(v) such ...

An (nk) configuration is a collection of points and straight lines, usually in the Euclidean plane, so that each point lies on k lines and each line passes through k points; such a configuration will be called symmetric if it possesses non-trivial geometric symmetry. Although examples of symmetric (n3) configurations with continuous parameters are known, to this point, all known connected infin...

the problem of navigation among movable obstacles (namo) is to find a collision free path for a robot while the robot is able to manipulate and transfer some objects (if possible or needed) to clear its path toward the goal. namo is a np-complete problem and is in a class of motion planning problems that have dynamic environments. in this domain, an optimal plan for the robot can be defined wit...

A 3D virtual space consists of non-movable and movable objects to provide more real environment, where movable objects can be transformed by translating, rotating and scaling. In most systems, the movement of objects can be performed by mice and keyboards. In this paper, we propose a controlling interface scheme for transforming the objects in the 3D virtual space based on gestures of left and ...

An exact hidden sphere algorithm that operates in linear time " , Comput