License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2018.60
URN: urn:nbn:de:0030-drops-90641
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Gärtner, Bernd ; Hansen, Thomas Dueholm ; Hubácek, Pavel ; Král, Karel ; Mosaad, Hagar ; Slívová, Veronika

ARRIVAL: Next Stop in CLS

LIPIcs-ICALP-2018-60.pdf (0.6 MB)


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.

BibTeX - Entry

  author =	{Bernd G{\"a}rtner and Thomas Dueholm Hansen and Pavel Hub{\'a}cek and Karel Kr{\'a}l and Hagar Mosaad and Veronika Sl{\'i}vov{\'a}},
  title =	{{ARRIVAL: Next Stop in CLS}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{60:1--60:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-90641},
  doi =		{10.4230/LIPIcs.ICALP.2018.60},
  annote =	{Keywords: CLS, switch graphs, zero-player game, UP n coUP}

Keywords: CLS, switch graphs, zero-player game, UP n coUP
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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