On the Complexity of Connection Games Edouard Bonnet, Florian Jamain, Abdallah Saffidine To cite this version: Edouard Bonnet, Florian Jamain, Abdallah Saffidine. On the Complexity of Connection Games. The- oretical Computer Science, Elsevier, 2016, 644, pp.2-28. 10.1016/j.tcs.2016.06.033. hal-01994450 HAL Id: hal-01994450 https://hal.archives-ouvertes.fr/hal-01994450 Submitted on 25 Jan 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. On the Complexity of Connection Games Édouard Bonnet
[email protected] Sztaki, Hungarian Academy of Sciences Florian Jamain
[email protected] Lamsade, Université Paris-Dauphine Abdallah Saffidine
[email protected] Cse, The University of New South Wales, Abstract In this paper, we study three connection games among the most widely played: havannah, twixt, and slither. We show that determining the outcome of an arbitrary input position is PSPACE-complete in all three cases. Our reductions are based on the popular graph problem generalized geography and on hex itself. We also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is W[1]-hard, short hex is FPT.