LIPIcs, Volume 291

12th International Conference on Fun with Algorithms (FUN 2024)



Thumbnail PDF

Event

FUN 2024, June 4-8, 2024, Island of La Maddalena, Sardinia, Italy

Editors

Andrei Z. Broder
  • Google
Tami Tamir
  • Reichman University, Herzliya, Israel

Publication Details

  • published at: 2024-05-29
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
  • ISBN: 978-3-95977-314-0
  • DBLP: db/conf/fun/fun2024

Access Numbers

Documents

No documents found matching your filter selection.
Document
Complete Volume
LIPIcs, Volume 291, FUN 2024, Complete Volume

Authors: Andrei Z. Broder and Tami Tamir


Abstract
LIPIcs, Volume 291, FUN 2024, Complete Volume

Cite as

12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 1-570, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@Proceedings{broder_et_al:LIPIcs.FUN.2024,
  title =	{{LIPIcs, Volume 291, FUN 2024, Complete Volume}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{1--570},
  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},
  URN =		{urn:nbn:de:0030-drops-199079},
  doi =		{10.4230/LIPIcs.FUN.2024},
  annote =	{Keywords: LIPIcs, Volume 291, FUN 2024, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Andrei Z. Broder and Tami Tamir


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{broder_et_al:LIPIcs.FUN.2024.0,
  author =	{Broder, Andrei Z. and Tamir, Tami},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{0:i--0:xvi},
  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.2024.0},
  URN =		{urn:nbn:de:0030-drops-199080},
  doi =		{10.4230/LIPIcs.FUN.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Baba Is Universal

Authors: Zachary Abel and Della Hendrickson


Abstract
We consider the computational complexity of constant-area levels of games which allow an unlimited number of objects in a fixed region. We discuss how to prove that such games are RE-hard (and in particular undecidable) and capable of universal computation, even on constant-area levels. We use the puzzle game Baba is You as a case study, showing that 8×17 levels are capable of universal computation by constructing a particular small universal counter machine within Baba is You.

Cite as

Zachary Abel and Della Hendrickson. Baba Is Universal. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{abel_et_al:LIPIcs.FUN.2024.1,
  author =	{Abel, Zachary and Hendrickson, Della},
  title =	{{Baba Is Universal}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{1:1--1:15},
  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.2024.1},
  URN =		{urn:nbn:de:0030-drops-199093},
  doi =		{10.4230/LIPIcs.FUN.2024.1},
  annote =	{Keywords: Undecidability, Baba is You, RE-hardness, counter machines, universal computation}
}
Document
Poset Positional Games

Authors: Guillaume Bagan, Eric Duchêne, Florian Galliot, Valentin Gledel, Mirjana Mikalački, Nacim Oijid, Aline Parreau, and Miloš Stojaković


Abstract
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an additional structure - a poset on the elements of the board. Throughout the game play, based on this poset and the set of the board elements that are claimed up to that point, we reduce the set of available moves for the player whose turn it is - an element of the board can only be claimed if all the smaller elements in the poset are already claimed. We proceed to analyze these games in more detail, with a prime focus on the most studied convention, the Maker-Breaker games. First we build a general framework around poset positional games. Then, we perform a comprehensive study of the complexity of determining the game outcome, conditioned on the structure of the family of winning sets on the one side and the structure of the poset on the other.

Cite as

Guillaume Bagan, Eric Duchêne, Florian Galliot, Valentin Gledel, Mirjana Mikalački, Nacim Oijid, Aline Parreau, and Miloš Stojaković. Poset Positional Games. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{bagan_et_al:LIPIcs.FUN.2024.2,
  author =	{Bagan, Guillaume and Duch\^{e}ne, Eric and Galliot, Florian and Gledel, Valentin and Mikala\v{c}ki, Mirjana and Oijid, Nacim and Parreau, Aline and Stojakovi\'{c}, Milo\v{s}},
  title =	{{Poset Positional Games}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{2:1--2:12},
  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.2024.2},
  URN =		{urn:nbn:de:0030-drops-199100},
  doi =		{10.4230/LIPIcs.FUN.2024.2},
  annote =	{Keywords: Positional games, Maker-Breaker games, Game complexity, Poset, Connect 4}
}
Document
Snake in Optimal Space and Time

Authors: Philip Bille, Martín Farach-Colton, Inge Li Gørtz, and Ivor van der Hoog


Abstract
We revisit the classic game of Snake and ask the basic data structural question: how many bits does it take to represent the state of a snake game so that it can be updated in constant time? Our main result is a data structure that uses optimal space (within constant factors). To achieve our results, we introduce several interesting data structural techniques, including a decomposition technique for the problem, a tabulation scheme for encoding small subproblems, and a dynamic memory allocation scheme.

Cite as

Philip Bille, Martín Farach-Colton, Inge Li Gørtz, and Ivor van der Hoog. Snake in Optimal Space and Time. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{bille_et_al:LIPIcs.FUN.2024.3,
  author =	{Bille, Philip and Farach-Colton, Mart{\'\i}n and G{\o}rtz, Inge Li and van der Hoog, Ivor},
  title =	{{Snake in Optimal Space and Time}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{3:1--3:15},
  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.2024.3},
  URN =		{urn:nbn:de:0030-drops-199118},
  doi =		{10.4230/LIPIcs.FUN.2024.3},
  annote =	{Keywords: Data structure, Snake, Nokia, String Algorithms}
}
Document
Uniform-Budget Solo Chess with Only Rooks or Only Knights Is Hard

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


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

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)


Copy BibTex To Clipboard

@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}
}
Document
Swapping Mixed-Up Beers to Keep Them Cool

Authors: Davide Bilò, Maurizio Fiusco, Luciano Gualà, and Stefano Leucci


Abstract
There was a mix-up in Escher’s bar and n customers sitting at the same table have each received a beer ordered by somebody else in the party. The drinks can be rearranged by swapping them in pairs, but the eccentric table shape only allows drinks to be exchanged between people sitting on opposite sides of the table. We study the problem of finding the minimum number of swaps needed so that each customer receives its desired beer before it gets warm. Formally, we consider the Colored Token Swapping problem on complete bipartite graphs. This problem is known to be solvable in polynomial time when all ordered drinks are different [Yamanaka et al., FUN 2014], but no results are known for the more general case in which multiple people in the party can order the same beer. We prove that Colored Token Swapping on complete bipartite graphs is NP-hard and that it is fixed-parameter tractable when parameterized by the number of distinct types of beer served by the bar.

Cite as

Davide Bilò, Maurizio Fiusco, Luciano Gualà, and Stefano Leucci. Swapping Mixed-Up Beers to Keep Them Cool. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{bilo_et_al:LIPIcs.FUN.2024.5,
  author =	{Bil\`{o}, Davide and Fiusco, Maurizio and Gual\`{a}, Luciano and Leucci, Stefano},
  title =	{{Swapping Mixed-Up Beers to Keep Them Cool}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{5:1--5:18},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-199132},
  doi =		{10.4230/LIPIcs.FUN.2024.5},
  annote =	{Keywords: Colored Token Swapping, Complete Bipartite Graphs, Labeled Token Swapping, FPT Algorithms, NP-Hardness}
}
Document
Bottom-Up Rebalancing Binary Search Trees by Flipping a Coin

Authors: Gerth Stølting Brodal


Abstract
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for sequences of n insertions into an initially empty binary search tree, under the assumption that a tree only stores the elements and the tree structure without any additional balance information. Seidel (2009) presented a top-down randomized insertion algorithm, where insertions take expected O(lg² n) time, and the resulting trees have the same distribution as inserting a uniform random permutation into a binary search tree without rebalancing. Seidel states as an open problem if a similar result can be achieved with bottom-up insertions. In this paper we fail to answer this question. We consider two simple canonical randomized bottom-up insertion algorithms on binary search trees, assuming that an insertion is given the position where to insert the next element. The subsequent rebalancing is performed bottom-up in expected O(1) time, uses expected O(1) random bits, performs at most two rotations, and the rotations appear with geometrically decreasing probability in the distance from the leaf. For some insertion sequences the expected depth of each node is proved to be O(lg n). On the negative side, we prove for both algorithms that there exist simple insertion sequences where the expected depth is Ω(n), i.e., the studied rebalancing schemes are not competitive with (most) other rebalancing schemes in the literature.

Cite as

Gerth Stølting Brodal. Bottom-Up Rebalancing Binary Search Trees by Flipping a Coin. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{brodal:LIPIcs.FUN.2024.6,
  author =	{Brodal, Gerth St{\o}lting},
  title =	{{Bottom-Up Rebalancing Binary Search Trees by Flipping a Coin}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{6:1--6:15},
  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.2024.6},
  URN =		{urn:nbn:de:0030-drops-199143},
  doi =		{10.4230/LIPIcs.FUN.2024.6},
  annote =	{Keywords: Binary search tree, insertions, random rebalancing}
}
Document
Physical Ring Signature

Authors: Xavier Bultel


Abstract
Ring signatures allow members of a group (called ring) to sign a message anonymously within the group, which is chosen ad hoc at the time of signing (the members do not need to have interacted before). In this paper, we propose a physical version of ring signatures. Our signature is based on one-out-of-many signatures, a method used in many real cryptographic ring signatures. It consists of boxes containing coins locked with padlocks that can only be opened by a particular group member. To sign a message, a group member shakes the boxes of the other members of the group so that the coins are in a random state ("heads" or "tails", corresponding to bits 0 and 1), and opens their box to arrange the coins so that the exclusive "or" of the coins corresponds to the bits of the message they wish to sign. We present a prototype that can be used with coins, or with dice for messages encoded in larger (non-binary) alphabets. We suggest that this system can be used to explain ring signatures to the general public in a fun way. Finally, we propose a semi-formal analysis of the security of our signature based on real cryptographic security proofs.

Cite as

Xavier Bultel. Physical Ring Signature. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{bultel:LIPIcs.FUN.2024.7,
  author =	{Bultel, Xavier},
  title =	{{Physical Ring Signature}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{7:1--7:18},
  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.2024.7},
  URN =		{urn:nbn:de:0030-drops-199154},
  doi =		{10.4230/LIPIcs.FUN.2024.7},
  annote =	{Keywords: Physical Cryptography, Ring Signature, Anonymity}
}
Document
A Tractability Gap Beyond Nim-Sums: It’s Hard to Tell Whether a Bunch of Superstars Are Losers

Authors: Kyle Burke, Matthew Ferland, Svenja Huntemann, and Shanghua Teng


Abstract
In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we consider superstars, positions first introduced in Winning Ways where all options are nimbers. Extending Morris' classic result with hot games to tepid games, we prove that disjunctive sums of superstars are intractable to solve. This is striking as sums of nimbers can be computed in linear time. Our analyses also lead to a family of elegant board games with intriguing complexity, for which we present web-playable versions of the rulesets described within.

Cite as

Kyle Burke, Matthew Ferland, Svenja Huntemann, and Shanghua Teng. A Tractability Gap Beyond Nim-Sums: It’s Hard to Tell Whether a Bunch of Superstars Are Losers. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{burke_et_al:LIPIcs.FUN.2024.8,
  author =	{Burke, Kyle and Ferland, Matthew and Huntemann, Svenja and Teng, Shanghua},
  title =	{{A Tractability Gap Beyond Nim-Sums: It’s Hard to Tell Whether a Bunch of Superstars Are Losers}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{8:1--8:14},
  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.2024.8},
  URN =		{urn:nbn:de:0030-drops-199168},
  doi =		{10.4230/LIPIcs.FUN.2024.8},
  annote =	{Keywords: Combinatorial Game Theory, NP-hardness, Superstars}
}
Document
The Steady-States of Splitter Networks

Authors: Basile Couëtoux, Bastien Gastaldi, and Guyslain Naves


Abstract
We introduce splitter networks, which abstract the behavior of conveyor belts found in the video game Factorio. Based on this definition, we show how to compute the steady-state of a splitter network. Then, leveraging insights from the players community, we provide multiple designs of splitter networks capable of load-balancing among several conveyor belts, and prove that any load-balancing network on n belts must have Ω(n log n) nodes. Incidentally, we establish connections between splitter networks and various concepts including flow algorithms, flows with equality constraints, Markov chains and the Knuth-Yao theorem about sampling over rational distributions using a fair coin.

Cite as

Basile Couëtoux, Bastien Gastaldi, and Guyslain Naves. The Steady-States of Splitter Networks. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{couetoux_et_al:LIPIcs.FUN.2024.9,
  author =	{Cou\"{e}toux, Basile and Gastaldi, Bastien and Naves, Guyslain},
  title =	{{The Steady-States of Splitter Networks}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{9:1--9:14},
  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.2024.9},
  URN =		{urn:nbn:de:0030-drops-199174},
  doi =		{10.4230/LIPIcs.FUN.2024.9},
  annote =	{Keywords: Factorio, splitter networks, flow, balancer, steady-state}
}
Document
How Did They Design This Game? Swish: Complexity and Unplayable Positions

Authors: Antoine Dailly, Pascal Lafourcade, and Gaël Marcadet


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
Hamiltonian Paths and Cycles in NP-Complete Puzzles

Authors: Marnix Deurloo, Mitchell Donkers, Mieke Maarse, Benjamin G. Rin, and Karen Schutte


Abstract
We show that several pen-and-paper puzzles are NP-complete by giving polynomial-time reductions from the Hamiltonian path and Hamiltonian cycle problems on grid graphs with maximum degree 3. The puzzles include Dotchi Loop, Chains, Linesweeper, Arukone{}₃ (also called Numberlink₃), and Araf. In addition, we show that this type of proof can still be used to prove the NP-completeness of Dotchi Loop even when the available puzzle instances are heavily restricted. Together, these results suggest that this approach holds promise in general for finding NP-completeness proofs of many pen-and-paper puzzles.

Cite as

Marnix Deurloo, Mitchell Donkers, Mieke Maarse, Benjamin G. Rin, and Karen Schutte. Hamiltonian Paths and Cycles in NP-Complete Puzzles. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{deurloo_et_al:LIPIcs.FUN.2024.11,
  author =	{Deurloo, Marnix and Donkers, Mitchell and Maarse, Mieke and Rin, Benjamin G. and Schutte, Karen},
  title =	{{Hamiltonian Paths and Cycles in NP-Complete Puzzles}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{11:1--11:25},
  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.2024.11},
  URN =		{urn:nbn:de:0030-drops-199199},
  doi =		{10.4230/LIPIcs.FUN.2024.11},
  annote =	{Keywords: Hamiltonicity, NP-completeness, complexity theory, pen-and-paper puzzles}
}
Document
Card-Based Cryptography Meets Differential Privacy

Authors: Reo Eriguchi, Kazumasa Shinagawa, and Takao Murakami


Abstract
Card-based cryptography studies the problem of implementing cryptographic algorithms in a visual way using physical cards to demonstrate their security properties for those who are unfamiliar with cryptography. In this paper, we initiate the study of card-based implementations of differentially private mechanisms, which are a standard privacy-enhancing technique to publish statistics of databases while protecting the privacy of any particular individual. We start with giving the definition of differential privacy of card-based protocols. As a feasibility result, we present three kinds of protocols using standard binary cards for computing the sum of parties' binary inputs, f(x₁,…,x_n) = ∑ⁿ_{i=1} x_i for x_i ∈ {0,1}, under differential privacy. Our first protocol follows the framework of output perturbation, which provides differential privacy by adding noise to exact aggregation results. The protocol needs only two shuffles, and the overheads in the number of cards and the error bound are independent of the number n of parties. Our second and third protocols are based on Randomized Response, which adds noise to each input before aggregation. Compared to the first protocol, they improve the overheads in the number of cards and the error bound in terms of differential privacy parameters at the cost of incurring a multiplicative factor of n. To address a technical challenge of generating non-uniform noise using a finite number of cards, we propose a novel differentially private mechanism based on the hypergeometric distribution, which we believe may be of independent interest beyond applications to card-based cryptography.

Cite as

Reo Eriguchi, Kazumasa Shinagawa, and Takao Murakami. Card-Based Cryptography Meets Differential Privacy. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{eriguchi_et_al:LIPIcs.FUN.2024.12,
  author =	{Eriguchi, Reo and Shinagawa, Kazumasa and Murakami, Takao},
  title =	{{Card-Based Cryptography Meets Differential Privacy}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{12:1--12:20},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-199206},
  doi =		{10.4230/LIPIcs.FUN.2024.12},
  annote =	{Keywords: Card-based cryptography, Differential privacy, Secure computation}
}
Document
The Great Textual Hoax: Boosting Sampled String Matching with Fake Samples

Authors: Simone Faro, Francesco Pio Marino, Andrea Moschetto, Arianna Pavone, and Antonio Scardace


Abstract
Sampled String Matching is presented as an efficient solution to the string matching problem, aiming to tackle the space constraints of indexed string matching while purportedly reducing search times for online solutions. Despite the problem’s inception dating back to 1991, practical solutions have only recently emerged. These purportedly accelerate online searches by up to 35 times compared to conventional methods, achieved through a partial index occupying a mere 5% of the text size. This paper delves into the intricacies of one of the latest and most effective text sampling techniques, character distance sampling, which revolves around sampling distances between characters of a selected alphabet within the text. Specifically, we introduce fake samples while remaining honest! In other words, the study reveals that, interestingly, strategically introducing fake samples within the sampled sequence slashes the required index space by almost half, just avoid compromising the algorithm’s correctness. Additionally, since efficiency is everything, this approach, in turn, purportedly enhances the algorithm’s efficiency under specific conditions.

Cite as

Simone Faro, Francesco Pio Marino, Andrea Moschetto, Arianna Pavone, and Antonio Scardace. The Great Textual Hoax: Boosting Sampled String Matching with Fake Samples. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{faro_et_al:LIPIcs.FUN.2024.13,
  author =	{Faro, Simone and Marino, Francesco Pio and Moschetto, Andrea and Pavone, Arianna and Scardace, Antonio},
  title =	{{The Great Textual Hoax: Boosting Sampled String Matching with Fake Samples}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{13:1--13:17},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-199211},
  doi =		{10.4230/LIPIcs.FUN.2024.13},
  annote =	{Keywords: string matching, sampling}
}
Document
PackIt!: Gamified Rectangle Packing

Authors: Thomas Garrison, Marijn J. H. Heule, and Bernardo Subercaseaux


Abstract
We present and analyze PackIt!, a turn-based game consisting of packing rectangles on an n × n grid. PackIt! can be easily played on paper, either as a competitive two-player game or in solitaire fashion. On the t-th turn, a rectangle of area t or t+1 must be placed in the grid. In the two-player format of PackIt! whichever player places a rectangle last wins, whereas the goal in the solitaire variant is to perfectly pack the n × n grid. We analyze necessary conditions for the existence of a perfect packing over n × n, then present an automated reasoning approach that allows finding perfect games of PackIt! up to n = 50 which includes a novel SAT-encoding technique of independent interest, and conclude by proving an NP-hardness result.

Cite as

Thomas Garrison, Marijn J. H. Heule, and Bernardo Subercaseaux. PackIt!: Gamified Rectangle Packing. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{garrison_et_al:LIPIcs.FUN.2024.14,
  author =	{Garrison, Thomas and Heule, Marijn J. H. and Subercaseaux, Bernardo},
  title =	{{PackIt!: Gamified Rectangle Packing}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{14:1--14:19},
  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.2024.14},
  URN =		{urn:nbn:de:0030-drops-199226},
  doi =		{10.4230/LIPIcs.FUN.2024.14},
  annote =	{Keywords: PackIt!, rectangle packing, SAT, NP-hardness}
}
Document
Polyamorous Scheduling

Authors: Leszek Gąsieniec, Benjamin Smith, and Sebastian Wild


Abstract
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the underlying optimisation problem: Polyamorous Scheduling. In Polyamorous Scheduling, we are given an edge-weighted graph and try to find a periodic schedule of matchings in this graph such that the maximal weighted waiting time between consecutive occurrences of the same edge is minimised. We show that the problem is NP-hard and that there is no efficient approximation algorithm with a better ratio than 4/3 unless P = NP. On the positive side, we obtain an O(log n)-approximation algorithm; indeed, an O(log Δ)-approximation for Δ the maximum degree, i.e., the largest number of relationships of any individual. We also define a generalisation of density from the Pinwheel Scheduling Problem, "poly density", and ask whether there exists a poly-density threshold similar to the 5/6-density threshold for Pinwheel Scheduling [Kawamura, STOC 2024]. Polyamorous Scheduling is a natural generalisation of Pinwheel Scheduling with respect to its optimisation variant, Bamboo Garden Trimming. Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem, and opens up numerous avenues for further study of Polyamorous Scheduling.

Cite as

Leszek Gąsieniec, Benjamin Smith, and Sebastian Wild. Polyamorous Scheduling. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{gasieniec_et_al:LIPIcs.FUN.2024.15,
  author =	{G\k{a}sieniec, Leszek and Smith, Benjamin and Wild, Sebastian},
  title =	{{Polyamorous Scheduling}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{15:1--15:18},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-199234},
  doi =		{10.4230/LIPIcs.FUN.2024.15},
  annote =	{Keywords: Periodic scheduling, Pinwheel scheduling, Edge-coloring, Chromatic index, Approximation algorithms, Hardness of approximation}
}
Document
Tetris Is Not Competitive

Authors: Matthias Gehnen and Luca Venier


Abstract
In the video game Tetris, a player has to decide how to place pieces on a board that are revealed by the game one after another. We show that the missing information about the upcoming pieces is indeed crucial to a player’s success. We present a construction for piece sequences that force (online) players without or with a finite preview of upcoming pieces to lose while (offline) players who know the entire piece sequence can clear the board and continue to play. From a competitive analysis perspective, it follows that there cannot be any c-competitive online algorithm for various optimization goals in the context of playing Tetris. Furthermore, we improve existing results by providing a construction for piece sequences which force every player to lose for every possible board size with at least two columns. With this construction, we are also able to show that an instance with just 435 pieces is sufficient to force every player to lose on a standard-size board with ten columns and twenty rows.

Cite as

Matthias Gehnen and Luca Venier. Tetris Is Not Competitive. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{gehnen_et_al:LIPIcs.FUN.2024.16,
  author =	{Gehnen, Matthias and Venier, Luca},
  title =	{{Tetris Is Not Competitive}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{16:1--16:16},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-199242},
  doi =		{10.4230/LIPIcs.FUN.2024.16},
  annote =	{Keywords: Online Algorithms, Tetris}
}
Document
Computational Complexity of Matching Match Puzzle

Authors: Yuki Iburi and Ryuhei Uehara


Abstract
Various forms of graph coloring problems have been studied over the years in the society of graph theory. Recently, some original puzzles are popularized in Japanese 100-yen shops, and one of them can be formalized as a graph coloring problem in a natural way. However, this natural graph coloring problem has not been investigated in the context of the graph theory. In this paper, we investigate this puzzle as a graph coloring problem. We first prove that this graph coloring problem is NP-complete even when the graph is restricted to a path or a spider. In these cases, diameter of the graphs seems to play an important role for its difficulty. We then show that the problem can be solved in polynomial time when the graph is restricted to some graph classes of constant diameter.

Cite as

Yuki Iburi and Ryuhei Uehara. Computational Complexity of Matching Match Puzzle. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 17:1-17:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{iburi_et_al:LIPIcs.FUN.2024.17,
  author =	{Iburi, Yuki and Uehara, Ryuhei},
  title =	{{Computational Complexity of Matching Match Puzzle}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{17:1--17:10},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-199251},
  doi =		{10.4230/LIPIcs.FUN.2024.17},
  annote =	{Keywords: Graph coloring, Matching Match puzzle, NP-complete, polynomial-time solvable}
}
Document
Advanced Spikes `n' Stuff: An NP-Hard Puzzle Game in Which All Tutorials Are Efficiently Solvable

Authors: Christian Ikenmeyer and Dylan Khangure


Abstract
We adjust Alan Hazelden’s 2017 polynomial time solvable puzzle game Spikes `n' Stuff: We obtain the NP-complete puzzle game Advanced Spikes `n' Stuff with 3 trap types so that each strict subset of the traps results in a polynomial time solvable puzzle game. We think of this as a "hard game in which all tutorial levels are easy". The polynomial time algorithms for solving the tutorial games turn out to be quite different to each other. While numerous papers analyze the complexity of games and which game objects make a game NP-hard, our paper is the first to study a game where the NP-hardness can only be achieved by a combination of all game objects, assuming P differs from NP.

Cite as

Christian Ikenmeyer and Dylan Khangure. Advanced Spikes `n' Stuff: An NP-Hard Puzzle Game in Which All Tutorials Are Efficiently Solvable. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{ikenmeyer_et_al:LIPIcs.FUN.2024.18,
  author =	{Ikenmeyer, Christian and Khangure, Dylan},
  title =	{{Advanced Spikes `n' Stuff: An NP-Hard Puzzle Game in Which All Tutorials Are Efficiently Solvable}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{18:1--18:13},
  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.2024.18},
  URN =		{urn:nbn:de:0030-drops-199265},
  doi =		{10.4230/LIPIcs.FUN.2024.18},
  annote =	{Keywords: computational complexity, P vs NP, motion planning, games}
}
Document
Anarchy in the APSP: Algorithm and Hardness for Incorrect Implementation of Floyd-Warshall

Authors: Jaehyun Koo


Abstract
The celebrated Floyd-Warshall algorithm efficiently computes the all-pairs shortest path, and its simplicity made it a staple in computer science classes. Frequently, students discover a variant of this Floyd-Warshall algorithm by mixing up the loop order, ending up with the incorrect APSP matrix. This paper considers a computational problem of computing this incorrect APSP matrix. We will propose efficient algorithms for this problem and prove that this incorrect variant is APSP-complete.

Cite as

Jaehyun Koo. Anarchy in the APSP: Algorithm and Hardness for Incorrect Implementation of Floyd-Warshall. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 19:1-19:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{koo:LIPIcs.FUN.2024.19,
  author =	{Koo, Jaehyun},
  title =	{{Anarchy in the APSP: Algorithm and Hardness for Incorrect Implementation of Floyd-Warshall}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{19:1--19:11},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-199270},
  doi =		{10.4230/LIPIcs.FUN.2024.19},
  annote =	{Keywords: fine-grained complexity, recreational algorithms}
}
Document
Variations on the Tournament Problem

Authors: Fabrizio Luccio, Linda Pagli, and Nicola Santoro


Abstract
In 1883, Lewis Carrol wrote a newspaper article to criticize how the second best player was determined in a tennis tournament, and to suggest how such a task could be done correctly. This article has been taken by Donald Knuth as the inspiration for efficiently determining the smallest t elements of a totally ordered set of size n using k-comparisons. In the ensuing research, optimal algorithms for some low values of k and t have been established, by Knuth and Aigner; for k = 2 and t ≤ 3, a few new bounds have been established for special values of n. Surprisingly, very little else is known on this problem, in spite of its illustrious pedigree and its relationship to other classical problems (e.g., selection and sorting with k-sorters). Enticed by the undeniable beauty of the problem, and the obvious promise of fun, we have joined the investigative quest. The purpose of this paper is to share some new results obtained so far. We are glad to report advances in two directions.

Cite as

Fabrizio Luccio, Linda Pagli, and Nicola Santoro. Variations on the Tournament Problem. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 20:1-20:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{luccio_et_al:LIPIcs.FUN.2024.20,
  author =	{Luccio, Fabrizio and Pagli, Linda and Santoro, Nicola},
  title =	{{Variations on the Tournament Problem}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{20:1--20:11},
  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.2024.20},
  URN =		{urn:nbn:de:0030-drops-199280},
  doi =		{10.4230/LIPIcs.FUN.2024.20},
  annote =	{Keywords: algorithms, parallel algorithms, tournament, selection, ranking}
}
Document
PSPACE-Hard 2D Super Mario Games: Thirteen Doors

Authors: MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, and Matias Korman


Abstract
We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to be NP-hard (FUN 2014). Our reductions build door gadgets with open, close, and traverse traversals, in each case using mechanics unique to the game. While some of our door constructions are similar to those from FUN 2016, those for Super Mario Bros. 2, Super Mario Land 2, Super Mario World 2, and the New Super Mario Bros. series are quite different; notably, the Super Mario Bros. 2 door is extremely difficult. Doors remain elusive for just two 2D Mario games (Super Mario Land and Super Mario Run); we prove that these games are at least NP-hard.

Cite as

MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, and Matias Korman. PSPACE-Hard 2D Super Mario Games: Thirteen Doors. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.21,
  author =	{MIT Hardness Group and Ani, Hayashi and Demaine, Erik D. and Hall, Holden and Korman, Matias},
  title =	{{PSPACE-Hard 2D Super Mario Games: Thirteen Doors}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{21:1--21:19},
  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.2024.21},
  URN =		{urn:nbn:de:0030-drops-199295},
  doi =		{10.4230/LIPIcs.FUN.2024.21},
  annote =	{Keywords: video games, computational complexity, PSPACE}
}
Document
You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games

Authors: MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, Ricardo Ruiz, and Naveen Venkat


Abstract
We prove RE-completeness (and thus undecidability) of several 2D games in the Super Mario Bros. platform video game series: the New Super Mario Bros. series (original, Wii, U, and 2), and both Super Mario Maker games in all five game styles (Super Mario Bros. 1 and 3, Super Mario World, New Super Mario Bros. U, and Super Mario 3D World). These results hold even when we restrict to constant-size levels and screens, but they do require generalizing to allow arbitrarily many enemies at each location and onscreen, as well as allowing for exponentially large (or no) timer. In our Super Mario Maker reductions, we work within the standard screen size and use the property that the game engine remembers offscreen objects that are global because they are supported by "global ground". To prove these Mario results, we build a new theory of counter gadgets in the motion-planning-through-gadgets framework, and provide a suite of simple gadgets for which reachability is RE-complete.

Cite as

MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, Ricardo Ruiz, and Naveen Venkat. You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.22,
  author =	{MIT Hardness Group and Ani, Hayashi and Demaine, Erik D. and Hall, Holden and Ruiz, Ricardo and Venkat, Naveen},
  title =	{{You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{22:1--22:20},
  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.2024.22},
  URN =		{urn:nbn:de:0030-drops-199302},
  doi =		{10.4230/LIPIcs.FUN.2024.22},
  annote =	{Keywords: video games, computational complexity, undecidability}
}
Document
ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles

Authors: MIT Hardness Group, Josh Brunner, Lily Chung, Erik D. Demaine, Della Hendrickson, and Andy Tockman


Abstract
We prove that Hamiltonicity in maximum-degree-3 grid graphs (directed or undirected) is ASP-complete, i.e., it has a parsimonious reduction from every NP search problem (including a polynomial-time bijection between solutions). As a consequence, given k Hamiltonian cycles, it is NP-complete to find another; and counting Hamiltonian cycles is #P-complete. If we require the grid graph’s vertices to form a full m × n rectangle, then we show that Hamiltonicity remains ASP-complete if the edges are directed or if we allow removing some edges (whereas including all undirected edges is known to be easy). These results enable us to develop a stronger "T-metacell" framework for proving ASP-completeness of rectangular puzzles, which requires building just a single gadget representing a degree-3 grid-graph vertex. We apply this general theory to prove ASP-completeness of 37 pencil-and-paper puzzles where the goal is to draw a loop subject to given constraints: Slalom, Onsen-meguri, Mejilink, Detour, Tapa-Like Loop, Kouchoku, Icelom; Masyu, Yajilin, Nagareru, Castle Wall, Moon or Sun, Country Road, Geradeweg, Maxi Loop, Mid-loop, Balance Loop, Simple Loop, Haisu, Reflect Link, Linesweeper; Vertex/Touch Slitherlink, Dotchi-Loop, Ovotovata, Building Walk, Rail Pool, Disorderly Loop, Ant Mill, Koburin, Mukkonn Enn, Rassi Silai, (Crossing) Ichimaga, Tapa, Canal View, and Aqre. The last 13 of these puzzles were not even known to be NP-hard. Along the way, we prove ASP-completeness of some simple forms of Tree-Residue Vertex-Breaking (TRVB), including planar multigraphs with degree-6 breakable vertices, or with degree-4 breakable and degree-1 unbreakable vertices.

Cite as

MIT Hardness Group, Josh Brunner, Lily Chung, Erik D. Demaine, Della Hendrickson, and Andy Tockman. ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.23,
  author =	{MIT Hardness Group and Brunner, Josh and Chung, Lily and Demaine, Erik D. and Hendrickson, Della and Tockman, Andy},
  title =	{{ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{23:1--23:20},
  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.2024.23},
  URN =		{urn:nbn:de:0030-drops-199314},
  doi =		{10.4230/LIPIcs.FUN.2024.23},
  annote =	{Keywords: pencil-and-paper puzzles, computational complexity, parsimony}
}
Document
Tetris with Few Piece Types

Authors: MIT Hardness Group, Erik D. Demaine, Holden Hall, and Jeffery Li


Abstract
We prove NP-hardness and #P-hardness of Tetris clearing (clearing an initial board using a given sequence of pieces) with the Super Rotation System (SRS), even when the pieces are limited to any two of the seven Tetris piece types. This result is the first advance on a question posed twenty years ago: which piece sets are easy vs. hard? All previous Tetris NP-hardness proofs used five of the seven piece types. We also prove ASP-completeness of Tetris clearing, using three piece types, as well as versions of 3-Partition and Numerical 3-Dimensional Matching where all input integers are distinct. Finally, we prove NP-hardness of Tetris survival and clearing under the "hard drops only" and "20G" modes, using two piece types, improving on a previous "hard drops only" result that used five piece types.

Cite as

MIT Hardness Group, Erik D. Demaine, Holden Hall, and Jeffery Li. Tetris with Few Piece Types. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.24,
  author =	{MIT Hardness Group and Demaine, Erik D. and Hall, Holden and Li, Jeffery},
  title =	{{Tetris with Few Piece Types}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{24:1--24:18},
  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.2024.24},
  URN =		{urn:nbn:de:0030-drops-199322},
  doi =		{10.4230/LIPIcs.FUN.2024.24},
  annote =	{Keywords: complexity, hardness, video games, counting}
}
Document
Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants

Authors: MIT Hardness Group, Della Hendrickson, and Andy Tockman


Abstract
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be NP-complete since 2000 [Kaye, 2000], but our framework proves it as a side effect. The second is inference: given a set of clues, is there any cell that the player can prove is safe? The coNP-completeness of this problem has been in the literature since 2011 [Scott et al., 2011], but we discovered a flaw that we believe is present in all published results, and we provide a fixed proof. Finally, the third is solvability: given the full state of a Minesweeper game, can the player win the game by safely clicking all non-mine cells? This problem has not yet been studied, and we prove that it is coNP-complete.

Cite as

MIT Hardness Group, Della Hendrickson, and Andy Tockman. Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.25,
  author =	{MIT Hardness Group and Hendrickson, Della and Tockman, Andy},
  title =	{{Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{25:1--25:20},
  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.2024.25},
  URN =		{urn:nbn:de:0030-drops-199335},
  doi =		{10.4230/LIPIcs.FUN.2024.25},
  annote =	{Keywords: NP, coNP, hardness, minesweeper, solvability, gadgets, simulation}
}
Document
Coordinating "7 Billion Humans" Is Hard

Authors: Alessandro Panconesi, Pietro Maria Posta, and Mirko Giacchini


Abstract
In the video game "7 Billion Humans", the player is requested to direct a group of workers to various destinations by writing a program that is executed simultaneously on each worker. While the game is quite rich and, indeed, it is considered one of the best games for beginners to learn the basics of programming, we show that even extremely simple versions are already NP-Hard or PSPACE-Hard.

Cite as

Alessandro Panconesi, Pietro Maria Posta, and Mirko Giacchini. Coordinating "7 Billion Humans" Is Hard. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{panconesi_et_al:LIPIcs.FUN.2024.26,
  author =	{Panconesi, Alessandro and Posta, Pietro Maria and Giacchini, Mirko},
  title =	{{Coordinating "7 Billion Humans" Is Hard}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{26:1--26:16},
  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.2024.26},
  URN =		{urn:nbn:de:0030-drops-199342},
  doi =		{10.4230/LIPIcs.FUN.2024.26},
  annote =	{Keywords: video games, computational complexity, NP, PSPACE}
}
Document
Arimaa Is PSPACE-Hard

Authors: Benjamin G. Rin and Atze Schipper


Abstract
Arimaa is a strategy board game developed in 2003 by Omar Syed, designed to be hard for AI to win because of its large branching factor. In this paper, its theoretical complexity is considered. We prove that Arimaa (suitably generalized to an n × n board) is PSPACE-hard. This result is found by reducing a known PSPACE-hard variant of Generalized Geography to a variant of Arimaa that we call Arimaa^′, which in turn is then reduced to (n × n) Arimaa. Since the game is easily seen to be solvable in exponential time, it follows that its complexity lies somewhere between being PSPACE-complete and EXPTIME-complete.

Cite as

Benjamin G. Rin and Atze Schipper. Arimaa Is PSPACE-Hard. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{rin_et_al:LIPIcs.FUN.2024.27,
  author =	{Rin, Benjamin G. and Schipper, Atze},
  title =	{{Arimaa Is PSPACE-Hard}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{27:1--27:24},
  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.2024.27},
  URN =		{urn:nbn:de:0030-drops-199359},
  doi =		{10.4230/LIPIcs.FUN.2024.27},
  annote =	{Keywords: Arimaa, complexity theory, PSPACE-hardness, board games, Generalized Geography}
}
Document
No Tiling of the 70 × 70 Square with Consecutive Squares

Authors: Jiří Sgall, János Balogh, József Békési, György Dósa, Lars Magnus Hvattum, and Zsolt Tuza


Abstract
The total area of the 24 squares of sizes 1,2,…,24 is equal to the area of the 70× 70 square. Can this equation be demonstrated by a tiling of the 70× 70 square with the 24 squares of sizes 1,2,…,24? The answer is "NO", no such tiling exists. This has been demonstrated by computer search. However, until now, no proof without use of computer was given. We fill this gap and give a complete combinatorial proof.

Cite as

Jiří Sgall, János Balogh, József Békési, György Dósa, Lars Magnus Hvattum, and Zsolt Tuza. No Tiling of the 70 × 70 Square with Consecutive Squares. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{sgall_et_al:LIPIcs.FUN.2024.28,
  author =	{Sgall, Ji\v{r}{\'\i} and Balogh, J\'{a}nos and B\'{e}k\'{e}si, J\'{o}zsef and D\'{o}sa, Gy\"{o}rgy and Hvattum, Lars Magnus and Tuza, Zsolt},
  title =	{{No Tiling of the 70 × 70 Square with Consecutive Squares}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{28:1--28:16},
  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.2024.28},
  URN =		{urn:nbn:de:0030-drops-199362},
  doi =		{10.4230/LIPIcs.FUN.2024.28},
  annote =	{Keywords: square packing, Gardner’s problem, combinatorial proof}
}
Document
Achieving the Highest Possible Elo Rating

Authors: Rikhav Shah


Abstract
Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor’s rating increases when they win and decreases when they lose. Increasing one’s rating can be difficult work; one must hone their skills and consistently beat the competition. Alternatively, with enough money you can rig the outcome of games to boost your rating. This paper poses a natural question for Elo rating systems: say you manage to get together n people (including yourself) and acquire enough money to rig k games. How high can you get your rating, asymptotically in k? In this setting, the people you gathered aren't very interested in the game, and will only play if you pay them to. This paper resolves the question for n = 2 up to constant additive error, and provides close upper and lower bounds for all other n, including for n growing arbitrarily with k. There is a phase transition at n = k^{1/3}: there is a huge increase in the highest possible Elo rating from n = 2 to n = k^{1/3}, but (depending on the particular Elo system used) little-to-no increase for any higher n. Past the transition point n > k^{1/3}, the highest possible Elo is at least Θ(k^{1/3}). The corresponding upper bound depends on the particular system used, but for the standard Elo system, is Θ(k^{1/3}log(k)^{1/3}).

Cite as

Rikhav Shah. Achieving the Highest Possible Elo Rating. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{shah:LIPIcs.FUN.2024.29,
  author =	{Shah, Rikhav},
  title =	{{Achieving the Highest Possible Elo Rating}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{29:1--29:21},
  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.2024.29},
  URN =		{urn:nbn:de:0030-drops-199376},
  doi =		{10.4230/LIPIcs.FUN.2024.29},
  annote =	{Keywords: Elo, rating system, monotonic invariant, Euler’s method, mass movement}
}
Document
How to Covertly and Uniformly Scramble the 15 Puzzle and Rubik’s Cube

Authors: Kazumasa Shinagawa, Kazuki Kanai, Kengo Miyamoto, and Koji Nuida


Abstract
A combination puzzle is a puzzle consisting of a set of pieces that can be rearranged into various combinations, such as the 15 Puzzle and Rubik’s Cube. Suppose a speedsolving competition for a combination puzzle is to be held. To make the competition fair, we need to generate an instance (i.e., a state having a solution) that is chosen uniformly at random and unknown to anyone. We call this problem a secure random instance generation of the puzzle. In this paper, we construct secure random instance generation protocols for the 15 Puzzle and for Rubik’s Cube. Our method is based on uniform cyclic group factorizations for finite groups, which is recently introduced by the same authors, applied to permutation groups for the puzzle instances. Specifically, our protocols require 19 shuffles for the 15 Puzzle and 43 shuffles for Rubik’s Cube.

Cite as

Kazumasa Shinagawa, Kazuki Kanai, Kengo Miyamoto, and Koji Nuida. How to Covertly and Uniformly Scramble the 15 Puzzle and Rubik’s Cube. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{shinagawa_et_al:LIPIcs.FUN.2024.30,
  author =	{Shinagawa, Kazumasa and Kanai, Kazuki and Miyamoto, Kengo and Nuida, Koji},
  title =	{{How to Covertly and Uniformly Scramble the 15 Puzzle and Rubik’s Cube}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{30:1--30:15},
  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.2024.30},
  URN =		{urn:nbn:de:0030-drops-199385},
  doi =		{10.4230/LIPIcs.FUN.2024.30},
  annote =	{Keywords: Card-based cryptography, Uniform cyclic group factorization, Secure random instance generation, The 15 Puzzle, Rubik’s Cube}
}
Document
A Programming Language Embedded in Magic: The Gathering

Authors: Howe Choong Yin and Alex Churchill


Abstract
Previous work demonstrated that the trading card game Magic: The Gathering is Turing complete, by embedding a universal Turing machine inside the game. However, this is extremely hard to program, and known programs are extremely inefficient. We demonstrate techniques for disabling Magic cards except when certain conditions are met, and use them to build a microcontroller with a versatile programming language embedded within a Magic game state. We remove all choices made by players, forcing all player moves except when a program instruction asks a player for input. This demonstrates Magic to be at least as complex as any two-player perfect knowledge game, which we demonstrate by supplying sample programs for Nim and the Collatz conjecture embedded in Magic. As with previous work, our result applies to how real Magic is played, and can be achieved using a tournament-legal deck; but the execution is far faster than previous constructions, generally one cycle of game turns per program instruction.

Cite as

Howe Choong Yin and Alex Churchill. A Programming Language Embedded in Magic: The Gathering. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{yin_et_al:LIPIcs.FUN.2024.31,
  author =	{Yin, Howe Choong and Churchill, Alex},
  title =	{{A Programming Language Embedded in Magic: The Gathering}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{31:1--31:19},
  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.2024.31},
  URN =		{urn:nbn:de:0030-drops-199391},
  doi =		{10.4230/LIPIcs.FUN.2024.31},
  annote =	{Keywords: Programming, computability theory, Magic: the Gathering, two-player games, tabletop games}
}
Document
Salon des Refusés
Eating Ice-Cream with a Colander

Authors: Kien Huynh and Valentin Polishchuk


Abstract
k-order α-hull is a generalization of both k-hull and α-shape (which are generalizations of convex hull); since its introduction in a 2014 IPL paper (which also established its combinatorial properties and gave efficient algorithms to compute it), it was used in a variety of applications (as witnessed by 38 citations in Google Scholar) ranging from computer graphics to hydrology to seismology. The subject must have been so rich and complex that it took more than a year to review the submission at IPL (which was chosen as the venue "Devoted to the Rapid Publication"), as may be witnessed by the timeline in the paper header. Nonetheless it was not rich enough to warrant publication at SODA 2009 and WADS 2009 (the reviews saying it is not yet ready for the prime time - cited from memory) nor in FUN 2010 to which the paper was submitted under the title "Eating Ice-Cream with Colander"

Cite as

Kien Huynh and Valentin Polishchuk. Eating Ice-Cream with a Colander. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 32:1-32:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{huynh_et_al:LIPIcs.FUN.2024.32,
  author =	{Huynh, Kien and Polishchuk, Valentin},
  title =	{{Eating Ice-Cream with a Colander}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{32:1--32:4},
  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.2024.32},
  URN =		{urn:nbn:de:0030-drops-199408},
  doi =		{10.4230/LIPIcs.FUN.2024.32},
  annote =	{Keywords: computational geometry, alpha-shape, k-hull, robust shape reconstruction}
}
Document
Salon des Refusés
Retrospective: Avoiding the Disk Bottleneck in the Data Domain Deduplication File System

Authors: Kai Li


Abstract
The paper titled "Avoiding the Disk Bottleneck in the Data Domain Deduplication File System" [Zhu et al., 2008] describes several fundamental ideas behind the file system that drives Data Domain’s deduplication storage products. Initially submitted to the 2007 ACM SIGOPS Symposium on Operating System Principles (SOSP), the paper was rejected by its program committee. It was subsequently submitted and accepted for publication at the USENIX Conference on File And Storage Technologies (FAST) in 2008. Twelve years later, it was honored with the USENIX Test-of-Time Award. This retrospective explores the paper’s historical significance and impact, analyzes the reasons behind its initial rejection, and suggests methods to enhance the paper review process in the academic community.

Cite as

Kai Li. Retrospective: Avoiding the Disk Bottleneck in the Data Domain Deduplication File System. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 33:1-33:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{li:LIPIcs.FUN.2024.33,
  author =	{Li, Kai},
  title =	{{Retrospective: Avoiding the Disk Bottleneck in the Data Domain Deduplication File System}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{33:1--33:4},
  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.2024.33},
  URN =		{urn:nbn:de:0030-drops-199417},
  doi =		{10.4230/LIPIcs.FUN.2024.33},
  annote =	{Keywords: Deduplication, file systems, compression}
}
Document
Salon des Refusés
Short Programs for Functions on Curves: A STOC Rejection

Authors: Victor S. Miller


Abstract
In 1986 I submitted a note "Short Programs for functions on curves" to the STOC conference. It was rejected. Since it seemed to be a paper that would only be interesting to a very small group of people, I didn't try to publish it, but instead circulated it among people who, I thought, would be interested in it. However, about 11 years later I was contacted by Dan Boneh, to whom I had given a copy a few years previously, who said that the algorithm in my paper had important applications. Since then it has become a core algorithm in the field of "Pairing Based Cryptography".

Cite as

Victor S. Miller. Short Programs for Functions on Curves: A STOC Rejection. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 34:1-34:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{miller:LIPIcs.FUN.2024.34,
  author =	{Miller, Victor S.},
  title =	{{Short Programs for Functions on Curves: A STOC Rejection}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{34:1--34:4},
  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.2024.34},
  URN =		{urn:nbn:de:0030-drops-199427},
  doi =		{10.4230/LIPIcs.FUN.2024.34},
  annote =	{Keywords: Elliptic Curves, Finite Fields, Weil Pairing, Straight Line Program}
}

Filters