The power of non-uniform wireless power

We study a fundamental measure for wireless interference in the SINR model known as (weighted) inductive independence. This measure characterizes the effectiveness of using oblivious power --- when the power used by a transmitter only depends on the distance to the receiver --- as a mechanism for improving wireless capacity. We prove optimal bounds for inductive independence, implying a number of algorithmic applications. An algorithm is provided that achieves --- due to existing lower bounds --- capacity that is asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems for oblivious power and for power control, including distributed scheduling, connectivity, secondary spectrum auctions, and dynamic packet scheduling.