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A sensor network consists of a collection of (possibly mobile) sensing devices that can coordinate their actions through wireless communication and aim at performing various tasks (e.g., surveillance, environmental monitoring) over a region sometimes referred to as the ldquomission spacerdquo. The performance of a sensor network is sensitive to the location of its nodes in the mission space. This leads to the basic ldquocoverage controlrdquo problem of properly, and possibly optimally, deploying sensors in order to meet the overall system's objectives. Clearly, to achieve such a goal, the nodes must share, at least partially, their state information. However, this may require a large amount of information exchange. Moreover, sensor nodes are frequently small, inexpensive devices with limited resources. Aside from energy required to move (if nodes are mobile), communication is known to be by far the largest consumer of the limited energy of a node, compared to other functions such as sensing and computation. Therefore, it is crucial to reduce communication between nodes to the minimum possible. This in turn imposes a constraint on the optimization task performed by each node, since it requires that actions be taken without full knowledge of other nodes' states. Standard synchronization schemes require that nodes periodically exchange state information which is clearly inefficient and, in fact, unnecessary since often the state of a node may not have changed much or may have only changed in a predictable way. This motivates us to seek not only distributed but also asynchronous optimization mechanisms in which a node communicates with others only when it considers it indispensable; in other words, each node tries to minimize the cost of communication by transmitting state information only under certain conditions and only as a last resort. This poses questions such as ldquowhat should the conditions be for a node to take such communication actions?rdquo and ldquounde- r what conditions, if any, can we guarantee that the resulting optimization scheme possesses desirable properties such as convergence to an optimum?"