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DOI: 10.4230/LIPIcs.FUN.2024.4
Uniform-Budget Solo Chess with Only Rooks or Only Knights Is Hard

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

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

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)

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@InProceedings{bilo_et_al:LIPIcs.FUN.2024.4,
  author =	{Bil\`{o}, Davide and Di Donato, Luca and Gual\`{a}, Luciano and Leucci, Stefano},
  title =	{{Uniform-Budget Solo Chess with Only Rooks or Only Knights Is Hard}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.4},
  URN =		{urn:nbn:de:0030-drops-199121},
  doi =		{10.4230/LIPIcs.FUN.2024.4},
  annote =	{Keywords: solo chess, puzzle games, board games, NP-completeness}
}
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