Search Results

Documents authored by Dailly, Antoine

Document
DOI: 10.4230/LIPIcs.FUN.2024.10
How Did They Design This Game? Swish: Complexity and Unplayable Positions

Authors: Antoine Dailly, Pascal Lafourcade, and Gaël Marcadet

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

Abstract
Swish is a competitive pattern recognition card-based game, in which players are trying to find a valid cards superposition from a set of cards, called a "swish". By the nature of the game, one may expect to easily recover the logic of the Swish’s designers. However, no justification appears to explain the number of cards, of duplicates, but also under which circumstances no player can find a swish. In this work, we formally investigate Swish. In the commercial version of the game, we observe that there exist large sets of cards with no swish, and find a construction to generate large sets of cards without swish. More importantly, in the general case with larger cards, we prove that Swish is NP-complete.
Cite as

Antoine Dailly, Pascal Lafourcade, and Gaël Marcadet. How Did They Design This Game? Swish: Complexity and Unplayable Positions. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dailly_et_al:LIPIcs.FUN.2024.10,
  author =	{Dailly, Antoine and Lafourcade, Pascal and Marcadet, Ga\"{e}l},
  title =	{{How Did They Design This Game? Swish: Complexity and Unplayable Positions}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{10:1--10:19},
  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.2024.10},
  URN =		{urn:nbn:de:0030-drops-199185},
  doi =		{10.4230/LIPIcs.FUN.2024.10},
  annote =	{Keywords: Game, Complexity, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.12
Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond

Authors: Dibyayan Chakraborty, Antoine Dailly, Sandip Das, Florent Foucaud, Harmender Gahlawat, and Subir Kumar Ghosh

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
A path is isometric if it is a shortest path between its endpoints. In this article, we consider the graph covering problem Isometric Path Cover, where we want to cover all the vertices of the graph using a minimum-size set of isometric paths. Although this problem has been considered from a structural point of view (in particular, regarding applications to pursuit-evasion games), it is little studied from the algorithmic perspective. We consider Isometric Path Cover on chordal graphs, and show that the problem is NP-hard for this class. On the positive side, for chordal graphs, we design a 4-approximation algorithm and an FPT algorithm for the parameter solution size. The approximation algorithm is based on a reduction to the classic path covering problem on a suitable directed acyclic graph obtained from a breadth first search traversal of the graph. The approximation ratio of our algorithm is 3 for interval graphs and 2 for proper interval graphs. Moreover, we extend the analysis of our approximation algorithm to k-chordal graphs (graphs whose induced cycles have length at most k) by showing that it has an approximation ratio of k+7 for such graphs, and to graphs of treelength at most 𝓁, where the approximation ratio is at most 6𝓁+2.
Cite as

Dibyayan Chakraborty, Antoine Dailly, Sandip Das, Florent Foucaud, Harmender Gahlawat, and Subir Kumar Ghosh. Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2022.12,
  author =	{Chakraborty, Dibyayan and Dailly, Antoine and Das, Sandip and Foucaud, Florent and Gahlawat, Harmender and Ghosh, Subir Kumar},
  title =	{{Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.12},
  URN =		{urn:nbn:de:0030-drops-172974},
  doi =		{10.4230/LIPIcs.ISAAC.2022.12},
  annote =	{Keywords: Shortest paths, Isometric path cover, Chordal graph, Interval graph, AT-free graph, Approximation algorithm, FPT algorithm, Treewidth, Chordality, Treelength}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact