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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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LIPIcs.FUN.2024.4.pdf
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Subject Classification

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.

Cite As Get BibTex

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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