On Improving Connectivity of Static Ad-Hoc Networks by Adding Nodes

Ad hoc networks are by nature constructed "automatically", by the nodes adapting to the neighboring nodes and building up a network. In this context, the network topology is random, and in particular, no connectivity is guaranteed: the nodes may be so sparsely located that they are unable to make up a connected network. This has motivated a wide range of research, with a primary interest in the connectivity of random networks. In this paper however, we are concerned with what can be done when an ad hoc network needs to be formed but the users are too far apart to form a network with a desired level of connectivity. More precisely, we study the option of improving the connectivity of a static ad-hoc network by carrying extraneous nodes to the scene. The problem is where to put these nodes so as to minimize the number of nodes required for a connected network, or to maximize the utility of the network. We present algorithms that suggest locations for such additional nodes. Networks where adding extraneous nodes is feasible are some sensor networks and such ad-hoc networks that are used in a controlled situation where some central entity can organize the deployment of the nodes. To our knowledge, the connectivity problem in ad hoc networks has not been addressed so far from this practical viewpoint. This paper is organized as follows: in the next section we describe the problem setting and the underlying assumptions, and define essentially two opti-