Pseudo-scheduling: A New Approach to the Broadcast Scheduling Problem
  The broadcast scheduling problem asks how a multihop network of broadcast transceivers operating on a shared medium may share the medium in such a way that communication over the entire network is possible. This can be naturally modeled as a graph coloring problem via distance-2 coloring (L(1,1)-labeling, strict scheduling). This coloring is difficult to compute and may require a number of colors quadratic in the graph degree. This paper introduces pseudo-scheduling, a relaxation of distance-2 coloring. Centralized and decentralized algorithms that compute pseudo-schedules with colors linear in the graph degree are given and proved. 
Shaun N. Joseph and Lisa C. DiPippo
cs.DS cs.NI math.CO