Counting the Number of Homonyms in Dynamic Networks

We consider a synchronous distributed system with n processes that communicate through a dynamic network guaranteeing 1-interval connectivity i.e., the network topology graph might change at each interval while keeping the graph connected at any time. The processes belonging to the distributed system are identified through a set of labels $\mathcal{L}=\{\ell_1, \ell_2 \dots, \ell_k\}$ (with 1 ≤ k < n). In this challenging system model, the paper addresses the following problem: "counting the number of processes with the same label". We provide a distributed algorithm that is able solve the problem based on the notion of energy transfer. Each process owns a fixed energy charge, and tries to discharge itself exchanging, at each round, at most half of its charge with neighbors. The paper also discusses when such counting is possible in the presence of failures. Counting processes with the same label in dynamic networks with homonyms is of great importance because it is as difficult as computing generic aggregating functions.