Brief announcement: efficient clustering in unstructured radio networks

Before any reasonable communication can be carried out in an ad-hoc/sensor network, nodes must establish a MAC scheme which provides reliable point-to-point connections to higher-layer protocols. One prominent approach to solving this task is to partition the nodes into clusters, each node being either a cluster-head or having a cluster-head within its communication range. Clustering allows the formation of virtual backbones, enables efficient routing, and helps realizing spatial multiplexing in non-overlapping clusters. Modelling the network as a graph, clustering leads to the classic minimum dominating set (MDS) problem. To the best of our knowledge, all existing MDS algorithms, e.g. [2, 3] assume that the scheduling of transmissions is handled by an operational MAC layer. Studying clustering in absence of an established MAC layer highlights the chicken-and-egg problem of the initialization phase: A MAC layer (“chicken”) helps achieving a clustering (“egg”), and vice versa. The problem of initializing and structuring is of great importance in practice; even in a single-hop ad-hoc network such as Bluetooth and for few devices, the initialization tends to be slow. The harsh conditions of such networks before their initialization can be modelled as follows: • The network is multi-hop and therefore, effects such as the hidden terminal problem must not be neglected. • Nodes do not feature a collision detection mechanism and the sender does not know how many neighbors have correctly received its message. • Nodes wake-up asynchronously and they do not have access to a global clock. In a multi-hop ad-hoc environment, it is realistic to assume that some nodes wake up (e.g. become deployed, or switched on) later than others. Sleeping nodes do neither send nor receive any messages. • Nodes have no knowledge about the number of neighbors or their wake-up pattern. They only know a rough estimate n̂ for the total number of nodes n = |V |, which is necessary in order to obtain sublinear runtime [1].