Generating Random Graphs for Wireless Actuator Networks

Abstract

In this paper, we consider graphs created by actuators (people, robots, vehicles etc.) in sensor-actuator networks. Most simulation studies for wireless ad hoc and sensor networks use connected random unit disk graphs generated by placing nodes randomly and independently from each other. However, in real life networks are created by actuators in a cooperative manner. Usually certain restrictions are imposed during the placement of a new node in order to improve network connectivity and functionality. This article is an initial study on how connected actuator graphs (CAG) can be generated by fast algorithms and what kind of desirable characteristics can be achieved compared to completely random graphs, especially for sparse node densities. We describe several CAG generation schemes where the next node (actuator) position is selected based on the distribution of the nodes already placed. In our Minimum Degree Proximity algorithm (MIN-DPA), a new node is placed to be a neighbor of an existing node with the lowest degree (number of neighbors). In our Maximum Degree Proximity algorithm (MAX-DPA), a new node cannot be placed to increase the degree of any existing node over a pre-specified parameter limit. We show that these new algorithms are significantly faster than the well-known random unit graph generation scheme for sparse graphs. The graphs generated by these new schemes are not necessarily drawn from the same distribution as those generated by the independent node placement. Thus, we explore their properties by studying their average node degree and partition patterns.