Hive is PSPACE-Hard
Publication date
2026
Authors
Rin, Benjamin
Andel, Daniël I.
Editors
Advisors
Supervisors
Document Type
Part of book
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Abstract
Hive is an abstract strategy game played on a table with hexagonal pieces. First published in 2001, it was and continues to be highly popular among both casual and competitive players. In this paper, we show that for a suitably generalized version of the game, the computational problem of determining whether a given player in an arbitrary position has a winning strategy is PSPACE-hard. We do this by reduction from Formula Game, which is first reduced to an intermediate problem we call Formula Game Geography, after which the latter is reduced to our decision problem.
Keywords
Combinatorial games, Computational complexity, Formula Game, Generalized Geography, Hive, PSPACE-hardness
Citation
Rin, B & Andel, D I 2026, Hive is PSPACE-Hard. in 13th International Conference on Fun with Algorithms (FUN 2026)., 3, Leibniz International Proceedings in Informatics, vol. 366, Dagstuhl Publishing, pp. 3:1–3:20. https://doi.org/10.4230/LIPIcs.FUN.2026.3