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Documents authored by Fink, Simon Dominik

Document
DOI: 10.4230/LIPIcs.FUN.2026.26
Hexasort - the Complexity of Stacking Colors on Graphs

Authors: Linus Klocker and Simon Dominik Fink

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku [Takayuki Yato and Takahiro Seta, 2003], Candy Crush [Luciano Gualà et al., 2014], and Flood-It [Fellows et al., 2018]. A common theme among these widely played games is that their generalized decision versions are NP-hard, which is often thought of as a source of their inherent difficulty and addictive appeal to human players. In this paper, we study a popular single-player stacking game commonly known as Hexasort. The game can be modelled as placing colored stacks onto the vertices of a graph, where adjacent stacks of the same color merge and vanish according to deterministic rules. We prove that Hexasort is NP-hard, even when restricted to single-color stacks and progressively more constrained classes of graphs, culminating in strong NP-hardness on trees of either bounded height or degree. Towards fixed-parameter tractable algorithms, we identify settings in which the problem becomes polynomial-time solvable and present dynamic programming algorithms.
Cite as

Linus Klocker and Simon Dominik Fink. Hexasort - the Complexity of Stacking Colors on Graphs. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 26:1-26:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{klocker_et_al:LIPIcs.FUN.2026.26,
  author =	{Klocker, Linus and Fink, Simon Dominik},
  title =	{{Hexasort - the Complexity of Stacking Colors on Graphs}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{26:1--26:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.26},
  URN =		{urn:nbn:de:0030-drops-257457},
  doi =		{10.4230/LIPIcs.FUN.2026.26},
  annote =	{Keywords: Hexasort, offline color stacking on graphs, NP-complete, polynomial-time solvable, dynamic programming}
}
Artifact
Software
DOI: 10.4230/artifacts.25245
The (not-so) Bad Dominating Set Maker

Authors: Alexander Dobler, Simon Dominik Fink, and Mathis Rocton

Abstract
Cite as

Alexander Dobler, Simon Dominik Fink, Mathis Rocton. The (not-so) Bad Dominating Set Maker (Software, source code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-25245,
   title = {{The (not-so) Bad Dominating Set Maker}}, 
   author = {Dobler, Alexander and Fink, Simon Dominik and Rocton, Mathis},
   note = {Software, Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035], Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT22029], European Union’s Horizon 2020 research and innovation COFUND programme (LogiCS@TUWien, grant agreement No 101034440), Austrian Science Fund (FWF) grant [10.55776/Y1329], swhId: \href{https://archive.softwareheritage.org/swh:1:dir:77b0720cd14b92e8d17e114ccf5c1ea89f79dfc9;origin=https://github.com/Doblalex/pace2025;visit=swh:1:snp:db5069228cfc618259ba32a9fe127fd1cb8ef66f;anchor=swh:1:rev:9d5280950b6d22bf75cddbc5bb9d41303b5ba4da}{\texttt{swh:1:dir:77b0720cd14b92e8d17e114ccf5c1ea89f79dfc9}} (visited on 2025-12-15)},
   url = {https://github.com/Doblalex/pace2025},
   doi = {10.4230/artifacts.25245},
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2025.35
PACE Solver Description: Bad Dominating Set Maker

Authors: Alexander Dobler, Simon Dominik Fink, and Mathis Rocton

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Dominating Set and Hitting Set are two well-known NP-hard problems on graphs and hypergraphs, respectively. For Dominating Set, we seek a subset S of vertices of minimum size, such that every vertex has a neighbor in S. For Hitting Set, we require that this minimum size subset S intersects each hyperedge. We present Bad Dominating Set Maker, our solver for both problems posed in the exact tracks of the 2025 PACE Challenge. It uses reduction rules, dynamic programming on tree decompositions, and external Vertex Cover and SAT solvers.
Cite as

Alexander Dobler, Simon Dominik Fink, and Mathis Rocton. PACE Solver Description: Bad Dominating Set Maker. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 35:1-35:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.IPEC.2025.35,
  author =	{Dobler, Alexander and Fink, Simon Dominik and Rocton, Mathis},
  title =	{{PACE Solver Description: Bad Dominating Set Maker}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{35:1--35:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.35},
  URN =		{urn:nbn:de:0030-drops-251673},
  doi =		{10.4230/LIPIcs.IPEC.2025.35},
  annote =	{Keywords: Dominating Set, Hitting Set, Pace Challenge}
}
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