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Constant Space and Non-Constant Time in Distributed Computing Lempiäinen, Tuomo Suomela, Jukka distributed computing space complexity constant-space algorithms weak models Thue-Morse sequence While the relationship of time and space is an established topic in traditional centralised com- plexity 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 com- puting. 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 show that indeed, there exist non-trivial graph problems that are solvable by constant-space algorithms but that require a non-constant running time. Somewhat surprisingly, this holds even when restricted to the class of only cycle and path graphs. Our work 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tuomo Lempiäinen and Jukka Suomela 2018 Is Part Of LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.OPODIS.2017.30 urn:nbn:de:0030-drops-86368 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.30 eng https://creativecommons.org/licenses/by/3.0/legalcode