Deterministic size discovery and topology recognition in radio networks with short labels

Abstract

We consider size discovery and topology recognition in radio networks without collision detection, modeled by simple undirected connected graphs. The aim of size discovery is that all nodes output the number of nodes in the graph, and in the task of topology recognition, each node has to learn the topology of the graph and its position in it. Nodes are assigned labels which are (not necessarily different) binary strings. Each node uses its own label as input when executing the algorithm. The length of a labeling scheme is the largest length of a label. Our goal is to construct short labeling schemes for size discovery and topology recognition in arbitrary radio networks, and to design efficient deterministic distributed algorithms for each of these tasks, using these short schemes. In both cases, the length of our labeling schemes is asymptotically optimal.