Infinite networks, halting and local algorithms (Draft)

Abstract

The immediate past has witnessed an increasing amount of interest in local algorithms, i.e., constant time distributed graph algorithms. In the recent survey of local algorithms (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms provide a framework that could be used in order to (theoretically) control infinitely large networks in finite time. We investigate halting of distributed algorithms from a theoretical point of view. We establish for a comprehensive collection of models of distributed computing that if infinite networks are included in the class of structures investigated, then every halting distributed algorithm is in fact a local algorithm. The models studied include various weak models of distributed computing in anonymous networks investigated by Hella and co-authors in (Hella et al., PODC 2012).