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Uniform-Budget Solo Chess with Only Rooks or Only Knights Is Hard

Authors Davide Bilò , Luca Di Donato, Luciano Gualà , Stefano Leucci

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Combinatorics
Keywords
  • solo chess
  • puzzle games
  • board games
  • NP-completeness

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Abstract

We study the Solo-Chess problem which has been introduced in [Aravind et al., FUN 2022]. This is a single-player variant of chess in which the player must clear all but one piece from the board via a sequence captures while ensuring that the number of captures performed by each piece does not exceed the piece’s budget. The time complexity of finding a winning sequence of captures has already been pinpointed for several combination of piece types and initial budgets. We contribute to a better understanding of the computational landscape of Solo-Chess by closing two problems left open in [Aravind et al., FUN 2022]. Namely, we show that Solo-Chess is hard even when all pieces are restricted to be only rooks with budget exactly 2, or only knights with budget exactly 11.

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Davide Bilò, Luca Di Donato, Luciano Gualà, and Stefano Leucci. Uniform-Budget Solo Chess with Only Rooks or Only Knights Is Hard. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FUN.2024.4

Author Details

Davide Bilò
  • Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy
Luca Di Donato
  • Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy
Luciano Gualà
  • Department of Enterprise Engineering, University of Rome "Tor Vergata", Italy
Stefano Leucci
  • Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy

References

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