73 Search Results for "Uehara, Ryuhei"

Volume

LIPIcs, Volume 157

10th International Conference on Fun with Algorithms (FUN 2021)

FUN 2021, May 30 to June 1, 2021, Favignana Island, Sicily, Italy

Editors: Martin Farach-Colton, Giuseppe Prencipe, and Ryuhei Uehara

Document
DOI: 10.4230/LIPIcs.SWAT.2026.10
Robotic Arm Rotation: Standing up Is Harder Than You Think

Authors: Nicolas Bousquet, Frank Connor, Remy El Sabeh, Louis-Roy Langevin, Amer E. Mouawad, Naomi Nishimura, and Agnes Totschnig

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We study motion-planning problems for planar robotic arms that rotate around fixed centers while avoiding collisions. In the SM-RAMP model, each unit-length arm may rotate at most once; the question is whether all arms can be rotated to the vertical position. We resolve an open problem of Bousquet et al. [Bousquet et al., 2026] by proving that SM-RAMP is NP-complete, even in the horizontal-to-vertical setting. Our hardness proof uses a structural analysis of rotation-propagation chains and introduces a combinatorial abstraction of independent interest, the Lighthouse Propagation problem, which we show is itself NP-complete. We then consider the multi-move variant MM-RAMP, where each arm may rotate multiple times among a fixed set of allowed angles (or orientations). We prove that MM-RAMP is PSPACE-complete even when each arm has only a few allowed angles, in sharp contrast with the single-move case. Finally, we give two fixed-parameter tractable algorithms: for MAX-SM-RAMP parameterized by the number k of arms to be made vertical, and for 2A-MM-RAMP (restricted to horizontal and vertical) parameterized by the number 𝓁 of allowed rotations.
Cite as

Nicolas Bousquet, Frank Connor, Remy El Sabeh, Louis-Roy Langevin, Amer E. Mouawad, Naomi Nishimura, and Agnes Totschnig. Robotic Arm Rotation: Standing up Is Harder Than You Think. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bousquet_et_al:LIPIcs.SWAT.2026.10,
  author =	{Bousquet, Nicolas and Connor, Frank and El Sabeh, Remy and Langevin, Louis-Roy and Mouawad, Amer E. and Nishimura, Naomi and Totschnig, Agnes},
  title =	{{Robotic Arm Rotation: Standing up Is Harder Than You Think}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.10},
  URN =		{urn:nbn:de:0030-drops-260467},
  doi =		{10.4230/LIPIcs.SWAT.2026.10},
  annote =	{Keywords: search, optimization, robotics, robotic arms, parameterized complexity, computational geometry, combinatorial reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.43
Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs

Authors: Tsuri Farhana, Omrit Filtser, and Shalev Goldshtein

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We study unlabeled multi-robot motion planning for unit-disk robots in a polygonal environment. Although the problem is hard in general, polynomial-time solutions exist under appropriate separation assumptions on start and target positions. Solovey et al. (RSS'15) provide a near-optimal solution assuming that start/target positions must have pairwise distance at least 4, and at least √5≈2.236 from obstacles. This raises the question of whether polynomial-time algorithms can be obtained in even more densely packed environments. In this paper we present a generalized algorithm that achieve different trade-offs on the robots-separation and obstacles-separation bounds, all significantly improving upon the state of the art. Specifically, we obtain polynomial-time constant-approximation algorithms to minimize the total path length when (i) the robots-separation is 2 2/3 and the obstacles-separation is 1 2/3, or (ii) the robots-separation is ≈3.291 and the obstacles-separation ≈1.354. Additionally, we introduce a different strategy yielding a polynomial-time solution when the robots-separation is only 2, and the obstacles-separation is 3. Finally, we show that without any robots-separation assumption, obstacles-separation of at least 1.5 may be necessary for a solution to exist.
Cite as

Tsuri Farhana, Omrit Filtser, and Shalev Goldshtein. Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{farhana_et_al:LIPIcs.SoCG.2026.43,
  author =	{Farhana, Tsuri and Filtser, Omrit and Goldshtein, Shalev},
  title =	{{Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.43},
  URN =		{urn:nbn:de:0030-drops-258495},
  doi =		{10.4230/LIPIcs.SoCG.2026.43},
  annote =	{Keywords: multi-robot motion planning}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.5
Token Positional Games

Authors: Guillaume Bagan, Quentin Deschamps, Florian Galliot, Mirjana Mikalački, and Nacim Oijid

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

Abstract
The classical Maker-Breaker positional game is played on a board which is a hypergraph ℋ, with two players, Maker and Breaker, alternately claiming vertices of ℋ until all the vertices are claimed. When the game ends, Maker wins if she has claimed all the vertices of some edge of ℋ; otherwise, Breaker wins. Playing this game in real life can be done by placing tokens on the vertices of the board. In this paper, we study the unfortunate case in which one or both players do not have enough tokens to cover all the vertices and, as such, will have to move their tokens around at some point instead of placing new ones. There may be a bias, in that Maker and Breaker do not necessarily have the same amount of tokens. The present paper initiates the study of this generalization of positional games, called token positional games. A particularly interesting case is when Maker has a winning strategy in the classical game: what is the lowest number of tokens with which she still wins against Breaker’s unlimited stock? We notably show that, for k-uniform hypergraphs on an arbitrarily large number n of vertices, this number equals k if k ∈ {2,3} but can vary from k to Ω(n) if k ≥ 4. From an algorithmic point of view, PSPACE-hardness in general is inherited from classical positional games, but we get a polynomial-time algorithm to solve the case where Breaker only has one token. We also establish EXPTIME-completeness for a "token sliding" variation of the game.
Cite as

Guillaume Bagan, Quentin Deschamps, Florian Galliot, Mirjana Mikalački, and Nacim Oijid. Token Positional Games. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bagan_et_al:LIPIcs.FUN.2026.5,
  author =	{Bagan, Guillaume and Deschamps, Quentin and Galliot, Florian and Mikala\v{c}ki, Mirjana and Oijid, Nacim},
  title =	{{Token Positional Games}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{5:1--5:22},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-257240},
  doi =		{10.4230/LIPIcs.FUN.2026.5},
  annote =	{Keywords: positional games, token games, hypergraphs, algorithmic complexity}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.10
77 Shades of Grey

Authors: Quentin Bramas, Stéphane Devismes, Anaïs Durand, Pascal Lafourcade, and Anissa Lamani

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

Abstract
Bruce Wayne contacted us to help him develop a new surveillance technology for dark environments such as caves, using a swarm of Unmanned Aerial Vehicles (UAVs), called Batdroids. A Batdroid has no chirality, limited visibility, and a perfect clock to synchronize with the others. A Batdroid can produce 77 shades of grey in dark mode and four colors in light mode. In this paper, we propose two algorithms using three Batdroids to perpetually explore a finite 3D grid modeling a cave. The first algorithm operates in darkness, uses 77 shades of grey, and requires visibility range one. The second operates in light, uses four colors and visibility range two. We also prove that three is the optimal number of Batdroids required to solve Bruce Wayne’s challenge.
Cite as

Quentin Bramas, Stéphane Devismes, Anaïs Durand, Pascal Lafourcade, and Anissa Lamani. 77 Shades of Grey. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bramas_et_al:LIPIcs.FUN.2026.10,
  author =	{Bramas, Quentin and Devismes, St\'{e}phane and Durand, Ana\"{i}s and Lafourcade, Pascal and Lamani, Anissa},
  title =	{{77 Shades of Grey}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{10:1--10:19},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-257294},
  doi =		{10.4230/LIPIcs.FUN.2026.10},
  annote =	{Keywords: Mobile robots, grid exploration, perpetual exploration}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.11
An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle

Authors: Matteo Caporrella and Stefano Leucci

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

Abstract
We study the Torus Puzzle, a solitaire game in which the elements of an input m × n matrix need to be rearranged into a target configuration via a sequence of unit rotations (i.e., circular shifts) of rows and/or columns. Amano et al. proposed a more permissive variant of the above puzzle, where each row and column rotation can shift the involved elements by any amount of positions. The number of rotations needed to solve the original and the permissive variants of the puzzle are respectively known as the push number and the drag number, where the latter is always smaller than or equal to the former and admits an existential lower bound of Ω(mn). While this lower bound is matched by an O(mn) upper bound, the push number is not so well understood. Indeed, to the best of our knowledge, only an O(mn ⋅ max{m, n}) upper bound is currently known. In this paper, we provide an algorithm that solves the Torus Puzzle using O(mn ⋅ log max {m, n}) unit rotations in a model that is more restricted than that of the original puzzle. This implies a corresponding upper bound on the push number and reduces the gap between the known upper and lower bounds from Θ(max{m,n}) to Θ(log max{m, n}).
Cite as

Matteo Caporrella and Stefano Leucci. An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caporrella_et_al:LIPIcs.FUN.2026.11,
  author =	{Caporrella, Matteo and Leucci, Stefano},
  title =	{{An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{11:1--11:21},
  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.2026.11},
  URN =		{urn:nbn:de:0030-drops-257307},
  doi =		{10.4230/LIPIcs.FUN.2026.11},
  annote =	{Keywords: Torus puzzle, Push number, Permutation puzzles}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.12
A Bookworm Climbs up the Polynomial Hierarchy: Meta-Restoration Complexity in Arithmetic Puzzles

Authors: Brynmor Chapman, Lily Chung, Erik D. Demaine, Yota Irino, Della Hendrickson, Tonan Kamata, and Ryuhei Uehara

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

Abstract
In arithmetic puzzles, a partially specified arithmetic expression must be completed to make the computation valid. Arithmetical restoration puzzles require filling in missing digits, while cryptarithms involve assigning digits to letters. The Japanese term mushikui-zan ("bookwormed arithmetic") commonly refers to arithmetical restorations, where we imagine the missing digits have been eaten by a bookworm. Puzzle creator Yousuke Ikeda proposed a new type of puzzle in which a previously designed bookwormed arithmetic with multiplication - known to have a unique solution - has itself been "bookwormed", that is, partially erased. The goal is to restore the specified blanks so that the resulting bookwormed puzzle again has a unique solution. We further generalize this framework: for each k ≥ 2, we define level-k puzzles as those in which type-k blanks must be filled to make the resulting level-(k{-}1) puzzle uniquely solvable. We study the level-k versions of the Boolean satisfiability problem, and show that they form a hierarchy of Σ^P_k-complete decision problems, tightly matching the levels of the polynomial hierarchy. As applications, we show that the level-k arithmetical restoration problem with multiplication is Σ^P_k-complete, as is the level-k cryptarithm problem. On the positive side, we show that level-2 arithmetical restoration puzzles with addition are solvable in polynomial time.
Cite as

Brynmor Chapman, Lily Chung, Erik D. Demaine, Yota Irino, Della Hendrickson, Tonan Kamata, and Ryuhei Uehara. A Bookworm Climbs up the Polynomial Hierarchy: Meta-Restoration Complexity in Arithmetic Puzzles. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chapman_et_al:LIPIcs.FUN.2026.12,
  author =	{Chapman, Brynmor and Chung, Lily and Demaine, Erik D. and Irino, Yota and Hendrickson, Della and Kamata, Tonan and Uehara, Ryuhei},
  title =	{{A Bookworm Climbs up the Polynomial Hierarchy: Meta-Restoration Complexity in Arithmetic Puzzles}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{12:1--12:15},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-257311},
  doi =		{10.4230/LIPIcs.FUN.2026.12},
  annote =	{Keywords: arithmetical restoration, cryptarithms, polynomial hierarchy, uniqueness quantifier, puzzle complexity}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.25
Computational Complexity of Swish Is Solved

Authors: Takashi Horiyama, Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Akira Suzuki, Ryuhei Uehara, and Yutaro Yamaguchi

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

Abstract
Swish is a card game in which players are given cards having symbols (hoops and balls), and find a valid superposition of cards, called a "swish." Dailly, Lafourcade, and Marcadet (FUN 2024) studied a generalized version of Swish and showed that the problem is solvable in polynomial time with one symbol per card, while it is NP-complete with three or more symbols per card. In this paper, we resolve the previously open case of two symbols per card, which corresponds to the original game. We show that Swish is NP-complete for this case. Specifically, we prove the NP-hardness when the allowed transformations of cards are restricted to a single (horizontal or vertical) flip or 180-degree rotation, and extend the results to the original setting allowing all three transformations. In contrast, when neither transformation is allowed, we present a polynomial-time algorithm. Combining known and our results, we establish a complete characterization of the computational complexity of Swish with respect to both the number of symbols per card and the allowed transformations.
Cite as

Takashi Horiyama, Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Akira Suzuki, Ryuhei Uehara, and Yutaro Yamaguchi. Computational Complexity of Swish Is Solved. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 25:1-25:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{horiyama_et_al:LIPIcs.FUN.2026.25,
  author =	{Horiyama, Takashi and Ito, Takehiro and Kawahara, Jun and Minato, Shin-ichi and Suzuki, Akira and Uehara, Ryuhei and Yamaguchi, Yutaro},
  title =	{{Computational Complexity of Swish Is Solved}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{25:1--25:12},
  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.2026.25},
  URN =		{urn:nbn:de:0030-drops-257448},
  doi =		{10.4230/LIPIcs.FUN.2026.25},
  annote =	{Keywords: Swish, Computational complexity, Matching, Parity-constrained cycles}
}
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}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.32
Tetris Is Hard with Just One Piece Type

Authors: MIT Hardness Group, Josh Brunner, Erik D. Demaine, Della Hendrickson, and Jeffery Li

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

Abstract
We analyze the computational complexity of Tetris clearing (determining whether the player can clear an initial board using a given sequence of pieces) and survival (determining whether the player can avoid losing before placing all the given pieces in an initial board) when restricted to a single polyomino piece type. We prove, for any tetromino piece type P except for O, the NP-hardness of Tetris clearing and survival under the standard Super Rotation System (SRS), even when the input sequence consists of only a specified number of P pieces. These surprising results disprove a 23-year-old conjecture on the computational complexity of Tetris with only I pieces (although our result is only for a specific rotation system). As a corollary, we prove the NP-hardness of Tetris clearing when the sequence of pieces has to be able to be generated from a 7k-bag randomizer for any positive integer k ≥ 1. On the positive side, we give polynomial-time algorithms for Tetris clearing and survival when the input sequence consists of only dominoes, assuming a particular rotation model, solving a version of a 9-year-old open problem. Along the way, we give polynomial-time algorithms for Tetris clearing and survival with 1 × k pieces (for any fixed k), provided the top k-1 rows are initially empty, showing that our I NP-hardness result needs to have filled cells in the top three rows.
Cite as

MIT Hardness Group, Josh Brunner, Erik D. Demaine, Della Hendrickson, and Jeffery Li. Tetris Is Hard with Just One Piece Type. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2026.32,
  author =	{MIT Hardness Group and Brunner, Josh and Demaine, Erik D. and Hendrickson, Della and Li, Jeffery},
  title =	{{Tetris Is Hard with Just One Piece Type}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{32:1--32:22},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-257515},
  doi =		{10.4230/LIPIcs.FUN.2026.32},
  annote =	{Keywords: complexity, hardness, video games, counting}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.36
Turing Completeness of GNU find: From mkdir-Assisted Loops to Standalone Computation

Authors: Keigo Oka

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

Abstract
The Unix command find is among the first commands taught to beginners, yet remains indispensable for experienced engineers. In this paper, we demonstrate that find possesses unexpected computational power, establishing three Turing completeness results using the GNU implementation (a standard in Linux distributions). (1) find + mkdir is Turing complete. By encoding computational states as directory paths and using regex back-references to copy substrings, we simulate 2-tag systems using only the find and mkdir executables. (2) GNU find 4.9.0+ alone is Turing complete: by reading and writing to files during traversal, we simulate a two-counter machine without mkdir. (3) find + mkdir without regex back-references is still Turing complete: by a trick of encoding regex patterns directly into directory names, we achieve the same power. These results place find among the "surprisingly Turing-complete" systems, highlighting the hidden complexity within seemingly simple standard utilities.
Cite as

Keigo Oka. Turing Completeness of GNU find: From mkdir-Assisted Loops to Standalone Computation. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{oka:LIPIcs.FUN.2026.36,
  author =	{Oka, Keigo},
  title =	{{Turing Completeness of GNU find: From mkdir-Assisted Loops to Standalone Computation}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{36:1--36:16},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-257555},
  doi =		{10.4230/LIPIcs.FUN.2026.36},
  annote =	{Keywords: Turing completeness, GNU find, tag system, counter machine}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.33
Higher Hardness Results for the Reconfiguration of Odd Matchings

Authors: Joseph Dorfer

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the reconfiguration of odd matchings of combinatorial graphs. Odd matchings are matchings that cover all but one vertex of a graph. A reconfiguration step, or flip, is an operation that matches the isolated vertex and, consequently, isolates another vertex. The flip graph of odd matchings is a graph that has all odd matchings of a graph as vertices and an edge between two vertices if their corresponding matchings can be transformed into one another via a single flip. We show that computing the diameter of the flip graph of odd matchings is Π₂^p-hard. This complements a recent result by Wulf [FOCS25] that it is Π₂^p-hard to compute the diameter of the flip graph of perfect matchings where a flip swaps matching edges along a single cycle of unbounded size. Further, we show that computing the radius of the flip graph of odd matchings is Σ₃^p-hard. The respective decision problems for the diameter and the radius are also complete in the respective level of the polynomial hierarchy. This shows that computing the radius of the flip graph of odd matchings is provably harder than computing its diameter, unless the polynomial hierarchy collapses. Finally, we reduce set cover to the problem of finding shortest flip sequences. As a consequence, we show APX-hardness and that the problem cannot be approximated by a sublogarithmic factor. By doing so, we answer a question asked by Aichholzer, Brenner, Dorfer, Hoang, Perz, Rieck, and Verciani [GD25].
Cite as

Joseph Dorfer. Higher Hardness Results for the Reconfiguration of Odd Matchings. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dorfer:LIPIcs.STACS.2026.33,
  author =	{Dorfer, Joseph},
  title =	{{Higher Hardness Results for the Reconfiguration of Odd Matchings}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.33},
  URN =		{urn:nbn:de:0030-drops-255222},
  doi =		{10.4230/LIPIcs.STACS.2026.33},
  annote =	{Keywords: Graph Reconfiguration Problems, Flip Graphs, Polynomial Hierarchy, APX-hardness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.19
A Linear Kernel for Independent Set Reconfiguration in Planar Graphs

Authors: Nicolas Bousquet and Daniel W. Cranston

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Fix a positive integer r, and a graph G that is K_{3,r}-minor-free. Let I_s and I_t be two independent sets in G, each of size k. We begin with a "token" on each vertex of I_s and seek to move all tokens to I_t, by repeated "token jumping", removing a single token from one vertex and placing it on another vertex. We require that each intermediate arrangement of tokens again specifies an independent set of size k. Given G, I_s, and I_t, we ask whether there exists a sequence of token jumps that transforms I_s into I_t. When k is part of the input, this problem is known to be PSPACE-complete. But it was shown by Ito, Kamiński, and Ono [Ito et al., 2014] to be fixed-parameter tractable. That is, the problem can be solved in time f(k)⋅ P(n), for some function f and polynomial P, where n denotes the order of G. Here we strengthen the upper bound on the running time in terms of k by showing that the problem has a kernel of size linear in k. More precisely, we transform an arbitrary input problem on a K_{3,r}-minor-free graph (for some fixed positive integer r) into an equivalent problem on a (K_{3,r}-minor-free) graph with order O(k). This answers positively a question of Bousquet, Mouawad, Nishimura, and Siebertz [Nicolas Bousquet et al., 2022] and improves the recent quadratic kernel of Cranston, Mühlenthaler, and Peyrille [Daniel W. Cranston et al., 2024]. For planar graphs, we further strengthen this upper bound to get a kernel of size at most 42k.
Cite as

Nicolas Bousquet and Daniel W. Cranston. A Linear Kernel for Independent Set Reconfiguration in Planar Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bousquet_et_al:LIPIcs.STACS.2026.19,
  author =	{Bousquet, Nicolas and Cranston, Daniel W.},
  title =	{{A Linear Kernel for Independent Set Reconfiguration in Planar Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.19},
  URN =		{urn:nbn:de:0030-drops-255081},
  doi =		{10.4230/LIPIcs.STACS.2026.19},
  annote =	{Keywords: Reconfiguration, Independent Set, Kernel, Planar graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.47
Dudeney’s Dissection Is Optimal

Authors: Erik D. Demaine, Tonan Kamata, and Ryuhei Uehara

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
In 1907, Henry Ernest Dudeney posed a puzzle: "cut any equilateral triangle ... into as few pieces as possible that will fit together and form a perfect square" (without overlap, via translation and rotation). Four weeks later, Dudeney demonstrated a beautiful four-piece solution, which today remains perhaps the most famous example of dissection. In this paper (over a century later), we finally solve Dudeney’s puzzle, by proving that the equilateral triangle and square have no common dissection with three or fewer polygonal pieces. We reduce the problem to the analysis of discrete graph structures representing the correspondence between the edges and the vertices of the pieces forming each polygon.
Cite as

Erik D. Demaine, Tonan Kamata, and Ryuhei Uehara. Dudeney’s Dissection Is Optimal. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{demaine_et_al:LIPIcs.ITCS.2026.47,
  author =	{Demaine, Erik D. and Kamata, Tonan and Uehara, Ryuhei},
  title =	{{Dudeney’s Dissection Is Optimal}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.47},
  URN =		{urn:nbn:de:0030-drops-253345},
  doi =		{10.4230/LIPIcs.ITCS.2026.47},
  annote =	{Keywords: Geometric Dissection, Dudeney Dissection, Dissection with Fewest Pieces}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.30
A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers

Authors: Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler

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

Abstract
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.
Cite as

Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler. A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beisegel_et_al:LIPIcs.IPEC.2025.30,
  author =	{Beisegel, Jesse and Klost, Katharina and Knorr, Kristin and Ratajczak, Fabienne and Scheffler, Robert},
  title =	{{A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{30:1--30:19},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-251623},
  doi =		{10.4230/LIPIcs.IPEC.2025.30},
  annote =	{Keywords: Hamiltonian path, Hamiltonian cycle, partial order, graph width parameter, parameterized complexity}
}
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