Foundation of Reactive Local Topology Control

Abstract

We formalize the concept reactive (aka contention-based or beaconless) topology control and its underlying problem statement. By means of message complexity, we define the classes of O(k)- and Ω(k)-reactive topology control algorithms which allow us to distinguish reactive from conventional local approaches and to classify the former. Moreover, based on our formalisms we prove two fundamental propositions regarding the reactive computability of standard topology control structures. Thus, our contribution not only establishes a taxonomy for identification of research gaps, but constitutes a theoretical foundation for profound investigation of this algorithm classes' principal power.