Locality in wireless scheduling

Locality is one of the fundamental issues in computing, with particular resonance in distributed settings. When it comes to wireless communication, it is not only an issue of what can be computed by consulting with your neighbors, but whether what happens far away can adversely affect whether you can actually do your work. With increasing attention to fading models of interference, such as the SINR model, lack of locality in communication has risen to the fore. When models take into account and accumulate arbitrarily far away transmissions, everyone seems to be affected by everyone else. This apparently unavoidable non-locality effect has been frequently cited as an impediment to effective analysis of SINR algorithms, especially distributed (see, e.g., [5, 1, 3]). Our main result is that a useful form of locality can actually be achieved in the SINR model. Specifically, we define locality to mean that the combined interference of any reasonably sparse (say, feasible) instance on any link that is “well-separated” from the instance must be low. It turns out that this locality property depends directly on the power assignment used: locality holds if power increases strictly faster than the square of the intended transmission distance (but not beyond the socalled path-loss factor), and fails otherwise.