2026-07-20T11:57:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9064 2024-03-06T10:43:16Z ddc:004 open_access

ARRIVAL: Next Stop in CLS Gärtner, Bernd Hansen, Thomas Dueholm Hubácek, Pavel Král, Karel Mosaad, Hagar Slívová, Veronika CLS switch graphs zero-player game UP n coUP We study the computational complexity of Arrival, a zero-player game on n-vertex switch graphs introduced by Dohrau, Gärtner, Kohler, Matousek, and Welzl. They showed that the problem of deciding termination of this game is contained in NP n coNP. Karthik C. S. recently introduced a search variant of Arrival and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of Arrival. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of Arrival is in UP n coUP. Second, we prove that the search variant of Arrival is contained in CLS. Third, we give a randomized O(1.4143^n)-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the Arrival game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime O(c^n) with c<2. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Bernd Gärtner and Thomas Dueholm Hansen and Pavel Hubácek and Karel Král and Hagar Mosaad and Veronika Slívová 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.60 urn:nbn:de:0030-drops-90641 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.60 eng https://creativecommons.org/licenses/by/3.0/legalcode