The Power of Oblivious 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 capacity that is — due to existing lower bounds — asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems involving both oblivious power and arbitrary power control, including connectivity, secondary spectrum auctions, and dynamic packet scheduling. We also show that the price of oblivious power — the relative increase in capacity possible when using unconstrained power control — is only doubly logarithmic in the maximum link length.