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. 
Magnus M. Halldorsson, Stephan Holzer, Pradipta Mitra and Roger   Wattenhofer
cs.DS