A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 ؉ 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time n O ((s log s) 2 ).

A critical aspect of applications with wireless sensor networks is network lifetime. Battery-powered sensors are usable as long as they can communicate captured data to a processing node. Sensing and communications consume energy, therefore judicious power management and scheduling can effectively extend the operational time. One important class of wireless sensor applications of deployment of large number of sensors in an area for environmental monitoring. The data collected by the sensors is sent to a central node for processing. In this paper we propose an efficient method to achieve energy savings by organizing the sensor nodes into a maximum number of disjoint dominating sets (DDS) which are activated successively. Only the sensors from the active set are responsible for monitoring the target area and for disseminating the collected data. All other nodes are into a sleep mode, characterized by a low energy consumption. We define the maximum disjoint dominating sets problem and we design a heuristic that computes the sets. Theoretical analysis and performance evaluation results are presented to verify our approach.

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