Effective Wireless Scheduling via Hypergraph Sketches
Magnús M. Halldórsson, Tigran Tonoyan · SIAM Journal on Computing · 2021
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment, and rate adjustment? We propose the first framework for approximation algorithms in the physical model of wireless interference that addresses these questions in full in interference-limited networks. The approximations obtained are at most doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement or better. The key insight is the discovery that a properly chosen power assignment infers a form of locality, or tolerance to the interference of both shorter and longer communication links. This allows us to simplify the complex interference relationship of the physical model into a new form of conflict graphs, at a small cost. We also show that the approximation obtained is provably the best possible for any conflict graph formulation.