While the relationship of time and space is an established topic in traditional centralised complexity theory, this is not the case in distributed computing. We aim to remedy this by studying the time and space complexity of algorithms in a weak message-passing model of distributed computing. While a constant number of communication rounds implies a constant number of states visited during the execution, the other direction is not clear at all. We consider several graph families and show that indeed, there exist non-trivial graph problems that are solvable by constant-space algorithms but that require a non-constant running time. This provides us with a new complexity class for distributed computing and raises interesting questions about the existence of further combinations of time and space complexity.
James Aspnes, Alysson Bessani, Pascal Felber, and João Leitão (Eds.): 21st International Conference on Principles of Distributed Systems (OPODIS 2017), volume 95 of Leibniz International Proceedings in Informatics (LIPIcs), pages 30:1–30:16, Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2018