Conflict graphs and the SINR-capacity of the mean power scheme

The Capacity problem in wireless networks is to select a maximum cardinality feasible subset of a set of transmission requests or links, where a set of links is feasible if the corresponding transmissions can be done simultaneously without collisions. We consider two models of feasibility: the SINR (Signal to Interference and Noise Ratio) model and a special conflict graph model. We show that if a special power assignment method is used (called the mean power scheme), then the solutions of the Capacity problem in the two models differ by at most a constant factor for any set of links in a doubling metric space of small dimension. This is not true for other power assignment methods in general. This result, besides showing that the mean power scheme is scalable between different models (as opposed to other power schemes), also has the potential to yield new results in the SINR model, using tools from graph theory, which we demonstrate in several examples.