# Non Trivial Computations in Anonymous Dynamic Networks

- 2015

#### Abstract

In this paper we consider a static set of anonymous processes, i.e., they do not have distinguished IDs, that communicate with neighbors using a local broadcast primitive. The communication graph changes at each computational round with the restriction of being always connected, i.e., the network topology guarantees 1-interval connectivity. In such setting non trivial computations, i.e., answering to a predicate like " there exists at least one process with initial input a? " , are impossible. In a recent work, it has been conjectured that the impossibility holds even if a distinguished leader process is available within the computation. In this paper we prove that the conjecture is false. We show this result by implementing a deterministic leader-based terminating counting algorithm. In order to build our counting algorithm we first develop a counting technique that is time optimal on a family of dynamic graphs where each process has a fixed distance h from the leader and such distance does not change along rounds. Using this technique we build an algorithm that counts in anonymous 1-interval connected networks. 1 Introduction Highly dynamic distributed systems are attracting a lot of interest from the relevant research community [13, 7]. These models are well suited to study the new challenges introduced by distributed systems where there is an immanent dynamicity given by the presence of mobile devices, unstable communication links and environmental constraints. A critical element in such future distributed systems is the anonymity of the devices; the uniqueness of a process ID is not guaranteed due to operational limit (e.g., in highly dynamic networks maintaining unique IDs may be infeasible due to mobility and failure among processes [22]) or to maintaining user's privacy (e.g., where users may not wish to disclose information about their behavior [11]). In this paper we consider a static set of anonymous process |V |, this set of processes is connected by a dynamic communication graph that is governed by a fictional omniscient

**DOI:**10.4230/LIPIcs.OPODIS.2015.33