65 Search Results for "Prencipe, Giuseppe"

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

Volume

LIPIcs, Volume 100

9th International Conference on Fun with Algorithms (FUN 2018)

FUN 2018, June 13-15, 2018, La Maddalena, Italy

Editors: Hiro Ito, Stefano Leonardi, Linda Pagli, and Giuseppe Prencipe

Document
DOI: 10.4230/LIPIcs.OPODIS.2023.33
Black Hole Search in Dynamic Rings: The Scattered Case

Authors: Giuseppe A. Di Luna, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract
In this paper we investigate the problem of searching for a black hole in a dynamic graph by a set of scattered agents (i.e., the agents start from arbitrary locations of the graph). The black hole is a node that silently destroys any agent visiting it. This kind of malicious node nicely models network failures such as a crashed host or a virus that erases the visiting agents. The black hole search problem is solved when at least one agent survives, and it has the entire map of the graph with the location of the black hole. We consider the case in which the underlining graph is a dynamic 1-interval connected ring: a ring graph in which at each round at most one edge can be missing. We first show that the problem cannot be solved if the agents can only communicate by using a face-to-face mechanism: this holds for any set of agents of constant size, with respect to the size n of the ring. To circumvent this impossibility we consider agents equipped with movable pebbles that can be left on nodes as a form of communication with other agents. When pebbles are available, three agents can localize the black hole in O(n²) moves. We show that such a number of agents is optimal. We also show that the complexity is tight, that is Ω(n²) moves are required for any algorithm solving the problem with three agents, even with stronger communication mechanisms (e.g., a whiteboard on each node on which agents can write messages of unlimited size). To the best of our knowledge this is the first paper examining the problem of searching a black hole in a dynamic environment with scattered agents.
Cite as

Giuseppe A. Di Luna, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Black Hole Search in Dynamic Rings: The Scattered Case. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{diluna_et_al:LIPIcs.OPODIS.2023.33,
  author =	{Di Luna, Giuseppe A. and Flocchini, Paola and Prencipe, Giuseppe and Santoro, Nicola},
  title =	{{Black Hole Search in Dynamic Rings: The Scattered Case}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.33},
  URN =		{urn:nbn:de:0030-drops-195233},
  doi =		{10.4230/LIPIcs.OPODIS.2023.33},
  annote =	{Keywords: Black hole search, mobile agents, dynamic graph}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FUN.2021
LIPIcs, Volume 157, FUN 2021, Complete Volume

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

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
LIPIcs, Volume 157, FUN 2021, Complete Volume
Cite as

10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 1-416, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{farachcolton_et_al:LIPIcs.FUN.2021,
  title =	{{LIPIcs, Volume 157, FUN 2021, Complete Volume}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{1--416},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021},
  URN =		{urn:nbn:de:0030-drops-127602},
  doi =		{10.4230/LIPIcs.FUN.2021},
  annote =	{Keywords: LIPIcs, Volume 157, FUN 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FUN.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

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

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

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

10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{farachcolton_et_al:LIPIcs.FUN.2021.0,
  author =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.0},
  URN =		{urn:nbn:de:0030-drops-127613},
  doi =		{10.4230/LIPIcs.FUN.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.1
Tatamibari Is NP-Complete

Authors: Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m x n grid of cells, where each cell possibly contains a clue among ⊞, ⊟, ◫. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing ⊞ are square, rectangles containing ⊟ are strictly longer horizontally than vertically, rectangles containing ◫ are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
Cite as

Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch. Tatamibari Is NP-Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{adler_et_al:LIPIcs.FUN.2021.1,
  author =	{Adler, Aviv and Bosboom, Jeffrey and Demaine, Erik D. and Demaine, Martin L. and Liu, Quanquan C. and Lynch, Jayson},
  title =	{{Tatamibari Is NP-Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.1},
  URN =		{urn:nbn:de:0030-drops-127624},
  doi =		{10.4230/LIPIcs.FUN.2021.1},
  annote =	{Keywords: Nikoli puzzles, NP-hardness, rectangle covering}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.2
Collaborative Procrastination

Authors: Aris Anagnostopoulos, Aristides Gionis, and Nikos Parotsidis

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
The problem of inconsistent planning in decision making, which leads to undesirable effects such as procrastination, has been studied in the behavioral-economics literature, and more recently in the context of computational behavioral models. Individuals, however, do not function in isolation, and successful projects most often rely on team work. Team performance does not depend only on the skills of the individual team members, but also on other collective factors, such as team spirit and cohesion. It is not an uncommon situation (for instance, experienced by the authors while working on this paper) that a hard-working individual has the capacity to give a good example to her team-mates and motivate them to work harder. In this paper we adopt the model of Kleinberg and Oren (EC'14) on time-inconsistent planning, and extend it to account for the influence of procrastination within the members of a team. Our first contribution is to model collaborative work so that the relative progress of the team members, with respect to their respective subtasks, motivates (or discourages) them to work harder. We compare the total cost of completing a team project when the team members communicate with each other about their progress, with the corresponding cost when they work in isolation. Our main result is a tight bound on the ratio of these two costs, under mild assumptions. We also show that communication can either increase or decrease the total cost. We also consider the problem of assigning subtasks to team members, with the objective of minimizing the negative effects of collaborative procrastination. We show that whereas a simple problem of forming teams of two members can be solved in polynomial time, the problem of assigning n tasks to n agents is NP-hard.
Cite as

Aris Anagnostopoulos, Aristides Gionis, and Nikos Parotsidis. Collaborative Procrastination. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{anagnostopoulos_et_al:LIPIcs.FUN.2021.2,
  author =	{Anagnostopoulos, Aris and Gionis, Aristides and Parotsidis, Nikos},
  title =	{{Collaborative Procrastination}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.2},
  URN =		{urn:nbn:de:0030-drops-127634},
  doi =		{10.4230/LIPIcs.FUN.2021.2},
  annote =	{Keywords: time-inconsistent planning, computational behavioral science, collaborative work, collaborative environments}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.3
Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets

Authors: Joshua Ani, Jeffrey Bosboom, Erik D. Demaine, Yenhenii Diomidov, Dylan Hendrickson, and Jayson Lynch

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
A door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "open" and "close" tunnel sets the gadget’s state to open and closed, respectively, while the "traverse" tunnel can be traversed if and only if the door is in the open state. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of such door gadgets, removing the traditional need for crossover gadgets and thereby simplifying past PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend of Zelda, and Donkey Kong Country. Our result holds in all but one of the possible local planar embedding of the open, close, and traverse tunnels within a door gadget; in the one remaining case, we prove NP-hardness. We also introduce and analyze a simpler type of door gadget, called the self-closing door. This gadget has two states and only two tunnels, similar to the "open" and "traverse" tunnels of doors, except that traversing the traverse tunnel also closes the door. In a variant called the symmetric self-closing door, the "open" tunnel can be traversed if and only if the door is closed. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of either type of self-closing door. Then we apply this framework to prove new PSPACE-hardness results for several 3D Mario games and Sokobond.
Cite as

Joshua Ani, Jeffrey Bosboom, Erik D. Demaine, Yenhenii Diomidov, Dylan Hendrickson, and Jayson Lynch. Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ani_et_al:LIPIcs.FUN.2021.3,
  author =	{Ani, Joshua and Bosboom, Jeffrey and Demaine, Erik D. and Diomidov, Yenhenii and Hendrickson, Dylan and Lynch, Jayson},
  title =	{{Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.3},
  URN =		{urn:nbn:de:0030-drops-127642},
  doi =		{10.4230/LIPIcs.FUN.2021.3},
  annote =	{Keywords: gadgets, motion planning, hardness of games}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.4
Taming the Knight’s Tour: Minimizing Turns and Crossings

Authors: Juan Jose Besa, Timothy Johnson, Nil Mamano, and Martha C. Osegueda

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
We introduce two new metrics of "simplicity" for knight’s tours: the number of turns and the number of crossings. We give a novel algorithm that produces tours with 9.5n+O(1) turns and 13n+O(1) crossings on a n× n board, and we show lower bounds of (6-ε)n and 4n-O(1) on the respective problems of minimizing these metrics. Hence, our algorithm achieves approximation ratios of 19/12+o(1) and 13/4+o(1). We generalize our techniques to rectangular boards, high-dimensional boards, symmetric tours, odd boards with a missing corner, and tours for (1,4)-leapers. In doing so, we show that these extensions also admit a constant approximation ratio on the minimum number of turns, and on the number of crossings in most cases.
Cite as

Juan Jose Besa, Timothy Johnson, Nil Mamano, and Martha C. Osegueda. Taming the Knight’s Tour: Minimizing Turns and Crossings. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{besa_et_al:LIPIcs.FUN.2021.4,
  author =	{Besa, Juan Jose and Johnson, Timothy and Mamano, Nil and Osegueda, Martha C.},
  title =	{{Taming the Knight’s Tour: Minimizing Turns and Crossings}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.4},
  URN =		{urn:nbn:de:0030-drops-127654},
  doi =		{10.4230/LIPIcs.FUN.2021.4},
  annote =	{Keywords: Graph Drawing, Chess, Hamiltonian Cycle, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.5
Cutting Bamboo down to Size

Authors: Davide Bilò, Luciano Gualà, Stefano Leucci, Guido Proietti, and Giacomo Scornavacca

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
This paper studies the problem of programming a robotic panda gardener to keep a bamboo garden from obstructing the view of the lake by your house. The garden consists of n bamboo stalks with known daily growth rates and the gardener can cut at most one bamboo per day. As a computer scientist, you found out that this problem has already been formalized in [Gąsieniec et al., SOFSEM'17] as the Bamboo Garden Trimming (BGT) problem, where the goal is that of computing a perpetual schedule (i.e., the sequence of bamboos to cut) for the robotic gardener to follow in order to minimize the makespan, i.e., the maximum height ever reached by a bamboo. Two natural strategies are Reduce-Max and Reduce-Fastest(x). Reduce-Max trims the tallest bamboo of the day, while Reduce-Fastest(x) trims the fastest growing bamboo among the ones that are taller than x. It is known that Reduce-Max and Reduce-Fastest(x) achieve a makespan of O(log n) and 4 for the best choice of x = 2, respectively. We prove the first constant upper bound of 9 for Reduce-Max and improve the one for Reduce-Fastest(x) to (3+√5)/2 < 2.62 for x = 1+1/√5. Another critical aspect stems from the fact that your robotic gardener has a limited amount of processing power and memory. It is then important for the algorithm to be able to quickly determine the next bamboo to cut while requiring at most linear space. We formalize this aspect as the problem of designing a Trimming Oracle data structure, and we provide three efficient Trimming Oracles implementing different perpetual schedules, including those produced by Reduce-Max and Reduce-Fastest(x).
Cite as

Davide Bilò, Luciano Gualà, Stefano Leucci, Guido Proietti, and Giacomo Scornavacca. Cutting Bamboo down to Size. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bilo_et_al:LIPIcs.FUN.2021.5,
  author =	{Bil\`{o}, Davide and Gual\`{a}, Luciano and Leucci, Stefano and Proietti, Guido and Scornavacca, Giacomo},
  title =	{{Cutting Bamboo down to Size}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.5},
  URN =		{urn:nbn:de:0030-drops-127663},
  doi =		{10.4230/LIPIcs.FUN.2021.5},
  annote =	{Keywords: bamboo garden trimming, trimming oracles, approximation algorithms, pinwheel scheduling}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.6
Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots

Authors: Quentin Bramas, Pascal Lafourcade, and Stéphane Devismes

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In 2042, the exoplanet exploration program, launched in 2014 by NASA, finally discovers a new exoplanet so-called Poleless, due to the fact that it is not subject to any magnetism. A new generation of autonomous mobile robots, called M2C (for Melomaniac Myopic Chameleon), have been designed to find water on Poleless. To address this problem, we investigate optimal (w.r.t., visibility range and number of used colors) solutions to the infinite grid exploration problem (IGE) by a small team of M2C robots. Our first result shows that minimizing the visibility range and the number of used colors are two orthogonal issues: it is impossible to design a solution to the IGE problem that is optimal w.r.t. both parameters simultaneously. Consequently, we address optimality of these two criteria separately by proposing two algorithms; the former being optimal in terms of visibility range, the latter being optimal in terms of number of used colors. It is worth noticing that these two algorithms use a very small number of robots, respectively six and eight.
Cite as

Quentin Bramas, Pascal Lafourcade, and Stéphane Devismes. Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bramas_et_al:LIPIcs.FUN.2021.6,
  author =	{Bramas, Quentin and Lafourcade, Pascal and Devismes, St\'{e}phane},
  title =	{{Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.6},
  URN =		{urn:nbn:de:0030-drops-127674},
  doi =		{10.4230/LIPIcs.FUN.2021.6},
  annote =	{Keywords: Luminous Robots, Grid, Infinite Exploration, Treasure Search Problem}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.7
1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete

Authors: Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, and Avi Zeff

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
Consider n²-1 unit-square blocks in an n × n square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable - a variation of Rush Hour with only 1 × 1 cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle. By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically. Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color Subway Shuffle.
Cite as

Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, and Avi Zeff. 1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brunner_et_al:LIPIcs.FUN.2021.7,
  author =	{Brunner, Josh and Chung, Lily and Demaine, Erik D. and Hendrickson, Dylan and Hesterberg, Adam and Suhl, Adam and Zeff, Avi},
  title =	{{1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.7},
  URN =		{urn:nbn:de:0030-drops-127681},
  doi =		{10.4230/LIPIcs.FUN.2021.7},
  annote =	{Keywords: puzzles, sliding blocks, PSPACE-hardness}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.8
An Optimal Algorithm for Online Freeze-Tag

Authors: Josh Brunner and Julian Wellman

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, each frozen robot is not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than 7/3 for online freeze-tag, and posed the question of whether an O(1)-competitive algorithm exists. We provide a (1+√2)-competitive algorithm for online time-dependent freeze-tag, and show that this is the best possible: there does not exist an algorithm which achieves a lower competitive ratio on every metric space.
Cite as

Josh Brunner and Julian Wellman. An Optimal Algorithm for Online Freeze-Tag. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 8:1-8:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{brunner_et_al:LIPIcs.FUN.2021.8,
  author =	{Brunner, Josh and Wellman, Julian},
  title =	{{An Optimal Algorithm for Online Freeze-Tag}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{8:1--8:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.8},
  URN =		{urn:nbn:de:0030-drops-127693},
  doi =		{10.4230/LIPIcs.FUN.2021.8},
  annote =	{Keywords: Online algorithm, competitive ratio, freeze-tag}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.9
Magic: The Gathering Is Turing Complete

Authors: Alex Churchill, Stella Biderman, and Austin Herrick

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
Magic: The Gathering is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world Magic is at least as hard as the Halting Problem. This provides a positive answer to the question "is there a real-world game where perfect play is undecidable under the rules in which it is typically played?", a question that has been open for a decade [David Auger and Oliver Teytaud, 2012; Erik D. Demaine and Robert A. Hearn, 2009]. To do this, we present a methodology for embedding an arbitrary Turing machine into a game of Magic such that the first player is guaranteed to win the game if and only if the Turing machine halts. Our result applies to how real Magic is played, can be achieved using standard-size tournament-legal decks, and does not rely on stochasticity or hidden information. Our result is also highly unusual in that all moves of both players are forced in the construction. This shows that even recognising who will win a game in which neither player has a non-trivial decision to make for the rest of the game is undecidable. We conclude with a discussion of the implications for a unified computational theory of games and remarks about the playability of such a board in a tournament setting.
Cite as

Alex Churchill, Stella Biderman, and Austin Herrick. Magic: The Gathering Is Turing Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{churchill_et_al:LIPIcs.FUN.2021.9,
  author =	{Churchill, Alex and Biderman, Stella and Herrick, Austin},
  title =	{{Magic: The Gathering Is Turing Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.9},
  URN =		{urn:nbn:de:0030-drops-127706},
  doi =		{10.4230/LIPIcs.FUN.2021.9},
  annote =	{Keywords: Turing machines, computability theory, Magic: the Gathering, two-player games}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.10
Computational Fun with Sturdy and Flimsy Numbers

Authors: Trevor Clokie, Thomas F. Lidbetter, Antonio J. Molina Lovett, Jeffrey Shallit, and Leon Witzman

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
Following Stolarsky, we say that a natural number n is flimsy in base b if some positive multiple of n has smaller digit sum in base b than n does; otherwise it is sturdy . We develop algorithmic methods for the study of sturdy and flimsy numbers. We provide some criteria for determining whether a number is sturdy. Focusing on the case of base b = 2, we study the computational problem of checking whether a given number is sturdy, giving several algorithms for the problem. We find two additional, previously unknown sturdy primes. We develop a method for determining which numbers with a fixed number of 0’s in binary are flimsy. Finally, we develop a method that allows us to estimate the number of k-flimsy numbers with n bits, and we provide explicit results for k = 3 and k = 5. Our results demonstrate the utility (and fun) of creating algorithms for number theory problems, based on methods of automata theory.
Cite as

Trevor Clokie, Thomas F. Lidbetter, Antonio J. Molina Lovett, Jeffrey Shallit, and Leon Witzman. Computational Fun with Sturdy and Flimsy Numbers. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{clokie_et_al:LIPIcs.FUN.2021.10,
  author =	{Clokie, Trevor and Lidbetter, Thomas F. and Molina Lovett, Antonio J. and Shallit, Jeffrey and Witzman, Leon},
  title =	{{Computational Fun with Sturdy and Flimsy Numbers}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.10},
  URN =		{urn:nbn:de:0030-drops-127715},
  doi =		{10.4230/LIPIcs.FUN.2021.10},
  annote =	{Keywords: sturdy number, flimsy number, context-free grammar, finite automaton, enumeration}
}
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