Reception Capacity Through Perfect Domination

The capacity of wireless networks is a classic and important topic of study. Informally, the capacity of a network is simply the total amount of information which it can transfer. In the context of models of wireless radio networks, this has usually meant the total number of point-to-point messages which can be sent or received in one time step. This definition has seen intensive study in recent years, particularly with respect to more accurate models of radio networks such as the SINR model. This paper is motivated by an obvious fact: radio antennae are (at least traditionally) omnidirectional, and hence point-to-point connections are not necessarily the best definition of capacity. To fix this, we introduce a new definition of reception capacity as the maximum number of messages which can be received in one round, and show that this is related to a new optimization problem we call the Maximum Perfect Dominated Set (MaxPDS) problem. Using this relationship we give tight upper and lower bounds for approximating this capacity. We also analyze this notion of capacity under game-theoretic constraints, giving tight bounds on both the Price of Anarchy and the Price of Stability.