Volume

LIPIcs, Volume 221

1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)



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Event

SAND 2022, March 28-30, 2022, Virtual Conference

Editors

James Aspnes
  • Yale University, New Haven, Connecticut, USA
Othon Michail
  • University of Liverpool, UK

Publication Details

  • published at: 2022-04-29
  • Publisher: Schloss-Dagstuhl - Leibniz Zentrum für Informatik
  • ISBN: 978-3-95977-224-2
  • DBLP: db/conf/sand/sand2022

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Document
Complete Volume
LIPIcs, Volume 221, SAND 2022, Complete Volume

Authors: James Aspnes and Othon Michail


Abstract
LIPIcs, Volume 221, SAND 2022, Complete Volume

Cite as

James Aspnes and Othon Michail. LIPIcs, Volume 221, SAND 2022, Complete Volume. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 1-370, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@Proceedings{aspnes_et_al:LIPIcs.SAND.2022,
  title =	{{LIPIcs, Volume 221, SAND 2022, Complete Volume}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{1--370},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022},
  URN =		{urn:nbn:de:0030-drops-159412},
  doi =		{10.4230/LIPIcs.SAND.2022},
  annote =	{Keywords: LIPIcs, Volume 221, SAND 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: James Aspnes and Othon Michail


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

Cite as

James Aspnes and Othon Michail. Front Matter, Table of Contents, Preface, Conference Organization. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 0:i-0:xvi, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{aspnes_et_al:LIPIcs.SAND.2022.0,
  author =	{Aspnes, James and Michail, Othon},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.0},
  URN =		{urn:nbn:de:0030-drops-159426},
  doi =		{10.4230/LIPIcs.SAND.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk)

Authors: Kathrin Hanauer, Monika Henzinger, and Christian Schulz


Abstract
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.

Cite as

Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 1:1-1:47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.1,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Schulz, Christian},
  title =	{{Recent Advances in Fully Dynamic Graph Algorithms}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{1:1--1:47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.1},
  URN =		{urn:nbn:de:0030-drops-159434},
  doi =		{10.4230/LIPIcs.SAND.2022.1},
  annote =	{Keywords: fully dynamic graph algorithms, survey}
}
Document
Invited Talk
Algorithmic Problems on Temporal Graphs (Invited Talk)

Authors: Paul G. Spirakis


Abstract
Research on Temporal Graphs has expanded in the last few years. Most of the results till now, address problems related to the notion of Temporal Paths (and Temporal Connectivity). In this talk, we focus, instead, on problems whose main topic is not on Temporal Paths. In particular, we will discuss Temporal Vertex Covers, the notion of Temporal Transitivity, and also issues and models of stochastic temporal graphs. We believe that several algorithmic graph problems, not directly related to paths, can be raised in the temporal domain. This may motivate new research towards lifting more topics of algorithmic graph theory to the temporal case.

Cite as

Paul G. Spirakis. Algorithmic Problems on Temporal Graphs (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, p. 2:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{spirakis:LIPIcs.SAND.2022.2,
  author =	{Spirakis, Paul G.},
  title =	{{Algorithmic Problems on Temporal Graphs}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.2},
  URN =		{urn:nbn:de:0030-drops-159446},
  doi =		{10.4230/LIPIcs.SAND.2022.2},
  annote =	{Keywords: Temporal graph, stochastic temporal graph, vertex cover, temporal transitivity}
}
Document
Invited Talk
Networks, Dynamics, Algorithms, and Learning (Invited Talk)

Authors: Roger Wattenhofer


Abstract
Networks are notoriously difficult to understand, and adding dynamics does not help. Can the current wonder weapon of computation (yes, machine learning) come to the rescue? Unfortunately, learning with networks is generally not well understood. "Neural network networks" (better and less confusingly known as graph neural networks) can learn simple graph patterns, but they are a far cry from their impressive machine learning cousins in the image- or the game-domain. In my opinion, the most astonishing graph neural networks are in fact dealing with dynamic networks: They simulate sand (the granular material, not the symposium) quite naturally. In my talk, I will discuss and compare different computational objects and paradigms: networks, dynamics, algorithms, and learning. What are the differences? And what can they learn from each other? In the technical part of the talk, I will present DropGNN, our new algorithm-inspired approach for handling graph neural networks. But mostly I will vent about misunderstandings and mistakes, and I will propose open questions, and new research directions. DropGNN is joint work with Pál András Papp, Karolis Martinkus, and Lukas Faber, published at NeurIPS, December 2021.

Cite as

Roger Wattenhofer. Networks, Dynamics, Algorithms, and Learning (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, p. 3:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{wattenhofer:LIPIcs.SAND.2022.3,
  author =	{Wattenhofer, Roger},
  title =	{{Networks, Dynamics, Algorithms, and Learning}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.3},
  URN =		{urn:nbn:de:0030-drops-159451},
  doi =		{10.4230/LIPIcs.SAND.2022.3},
  annote =	{Keywords: graph neural networks}
}
Document
Atomic Splittable Flow Over Time Games

Authors: Antonia Adamik and Leon Sering


Abstract
In an atomic splittable flow over time game, finitely many players route flow dynamically through a network, in which edges are equipped with transit times, specifying the traversing time, and with capacities, restricting flow rates. Infinitesimally small flow particles controlled by the same player arrive at a constant rate at the player’s origin and the player’s goal is to maximize the flow volume that arrives at the player’s destination within a given time horizon. Here, the flow dynamics are described by the deterministic queuing model, i.e., flow of different players merges perfectly, but excessive flow has to wait in a queue in front of the bottle-neck. In order to determine Nash equilibria in such games, the main challenge is to consider suitable definitions for the players' strategies, which depend on the level of information the players receive throughout the game. For the most restricted version, in which the players receive no information on the network state at all, we can show that there is no Nash equilibrium in general, not even for networks with only two edges. However, if the current edge congestions are provided over time, the players can adapt their route choices dynamically. We show that a profile of those strategies always lead to a unique feasible flow over time. Hence, those atomic splittable flow over time games are well-defined. For parallel-edge networks Nash equilibria exists and the total flow arriving in time equals the value of a maximum flow over time leading to a price of anarchy of 1.

Cite as

Antonia Adamik and Leon Sering. Atomic Splittable Flow Over Time Games. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 4:1-4:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{adamik_et_al:LIPIcs.SAND.2022.4,
  author =	{Adamik, Antonia and Sering, Leon},
  title =	{{Atomic Splittable Flow Over Time Games}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.4},
  URN =		{urn:nbn:de:0030-drops-159462},
  doi =		{10.4230/LIPIcs.SAND.2022.4},
  annote =	{Keywords: Flows Over Time, Deterministic Queuing, Atomic Splittable Games, Equilibria, Traffic, Cooperation}
}
Document
Faster Exploration of Some Temporal Graphs

Authors: Duncan Adamson, Vladimir V. Gusev, Dmitriy Malyshev, and Viktor Zamaraev


Abstract
A temporal graph G = (G_1, G_2, ..., G_T) is a graph represented by a sequence of T graphs over a common set of vertices, such that at the i-th time step only the edge set E_i is active. The temporal graph exploration problem asks for a shortest temporal walk on some temporal graph visiting every vertex. We show that temporal graphs with n vertices can be explored in O(k n^{1.5} log n) days if the underlying graph has treewidth k and in O(n^{1.75} log n) days if the underlying graph is planar. Furthermore, we show that any temporal graph whose underlying graph is a cycle with k chords can be explored in at most 6kn days. Finally, we demonstrate that there are temporal realisations of sub cubic planar graphs that cannot be explored faster than in Ω(n log n) days. All these improve best known results in the literature.

Cite as

Duncan Adamson, Vladimir V. Gusev, Dmitriy Malyshev, and Viktor Zamaraev. Faster Exploration of Some Temporal Graphs. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 5:1-5:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{adamson_et_al:LIPIcs.SAND.2022.5,
  author =	{Adamson, Duncan and Gusev, Vladimir V. and Malyshev, Dmitriy and Zamaraev, Viktor},
  title =	{{Faster Exploration of Some Temporal Graphs}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{5:1--5:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.5},
  URN =		{urn:nbn:de:0030-drops-159475},
  doi =		{10.4230/LIPIcs.SAND.2022.5},
  annote =	{Keywords: Temporal Graphs, Graph Exploration}
}
Document
Building Squares with Optimal State Complexity in Restricted Active Self-Assembly

Authors: Robert M. Alaniz, David Caballero, Sonya C. Cirlos, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Armando Tenorio, and Tim Wylie


Abstract
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model has been shown to be powerful, but many fundamental questions have yet to be explored. Here, we study the state complexity of assembling n × n squares in seeded Tile Automata systems where growth starts from a seed and tiles may attach one at a time, similar to the abstract Tile Assembly Model. We provide optimal bounds for three classes of seeded Tile Automata systems (all without detachment), which vary in the amount of complexity allowed in the transition rules. We show that, in general, seeded Tile Automata systems require Θ(log^{1/4} n) states. For Single-Transition systems, where only one state may change in a transition rule, we show a bound of Θ(log^{1/3} n), and for deterministic systems, where each pair of states may only have one associated transition rule, a bound of Θ(({log n}/{log log n})^{1/2}).

Cite as

Robert M. Alaniz, David Caballero, Sonya C. Cirlos, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Armando Tenorio, and Tim Wylie. Building Squares with Optimal State Complexity in Restricted Active Self-Assembly. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 6:1-6:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{alaniz_et_al:LIPIcs.SAND.2022.6,
  author =	{Alaniz, Robert M. and Caballero, David and Cirlos, Sonya C. and Gomez, Timothy and Grizzell, Elise and Rodriguez, Andrew and Schweller, Robert and Tenorio, Armando and Wylie, Tim},
  title =	{{Building Squares with Optimal State Complexity in Restricted Active Self-Assembly}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.6},
  URN =		{urn:nbn:de:0030-drops-159482},
  doi =		{10.4230/LIPIcs.SAND.2022.6},
  annote =	{Keywords: Active Self-Assembly, State Complexity, Tile Automata}
}
Document
Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem

Authors: Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser


Abstract
We present a loosely-stabilizing phase clock for population protocols. In the population model we are given a system of n identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires O(log n) states. It runs forever and is, at any point of time, in a synchronous state w.h.p. When started in an arbitrary configuration, it recovers rapidly and enters a synchronous configuration within O(n log n) interactions w.h.p. Once the clock is synchronized, it stays in a synchronous configuration for at least poly(n) parallel time w.h.p. We use our clock to design a loosely-stabilizing protocol that solves the adaptive variant of the majority problem. We assume that the agents have either opinion A or B or they are undecided and agents can change their opinion at a rate of 1/n. The goal is to keep track which of the two opinions is (momentarily) the majority. We show that if the majority has a support of at least Ω(log n) agents and a sufficiently large bias is present, then the protocol converges to a correct output within O(n log n) interactions and stays in a correct configuration for poly(n) interactions, w.h.p.

Cite as

Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser. Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{berenbrink_et_al:LIPIcs.SAND.2022.7,
  author =	{Berenbrink, Petra and Biermeier, Felix and Hahn, Christopher and Kaaser, Dominik},
  title =	{{Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.7},
  URN =		{urn:nbn:de:0030-drops-159493},
  doi =		{10.4230/LIPIcs.SAND.2022.7},
  annote =	{Keywords: Population Protocols, Phase Clocks, Loose Self-stabilization, Clock Synchronization, Majority, Adaptive}
}
Document
Complexity of Verification in Self-Assembly with Prebuilt Assemblies

Authors: David Caballero, Timothy Gomez, Robert Schweller, and Tim Wylie


Abstract
We analyze the complexity of two fundamental verification problems within a generalization of the two-handed tile self-assembly model (2HAM) where initial system assemblies are not restricted to be singleton tiles, but may be larger pre-built assemblies. Within this model we consider the producibility problem, which asks if a given tile system builds, or produces, a given assembly, and the unique assembly verification (UAV) problem, which asks if a given system uniquely produces a given assembly. We show that producibility is NP-complete and UAV is coNP^{NP}-complete even when the initial assembly size and temperature threshold are both bounded by a constant. This is in stark contrast to results in the standard model with singleton input tiles where producibility is in P and UAV is in coNP for 𝒪(1) bounded temperature and coNP-complete when temperature is part of the input. We further provide preliminary results for producibility and UAV in the case of 1-dimensional linear assemblies with pre-built assemblies, and provide polynomial time solutions.

Cite as

David Caballero, Timothy Gomez, Robert Schweller, and Tim Wylie. Complexity of Verification in Self-Assembly with Prebuilt Assemblies. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 8:1-8:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{caballero_et_al:LIPIcs.SAND.2022.8,
  author =	{Caballero, David and Gomez, Timothy and Schweller, Robert and Wylie, Tim},
  title =	{{Complexity of Verification in Self-Assembly with Prebuilt Assemblies}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.8},
  URN =		{urn:nbn:de:0030-drops-159503},
  doi =		{10.4230/LIPIcs.SAND.2022.8},
  annote =	{Keywords: 2-handed assembly, verification, prebuilt}
}
Document
Robustness of Distances and Diameter in a Fragile Network

Authors: Arnaud Casteigts, Timothée Corsini, Hervé Hocquard, and Arnaud Labourel


Abstract
A property of a graph G is robust if it remains unchanged in all connected spanning subgraphs of G. This form of robustness is motivated by networking contexts where some links eventually fail permanently, and the network keeps being used so long as it is connected. It is then natural to ask how certain properties of the network may be impacted as the network deteriorates. In this paper, we focus on two particular properties, which are the diameter, and pairwise distances among nodes. Surprisingly, the complexities of deciding whether these properties are robust are quite different: deciding the robustness of the diameter is coNP-complete, whereas deciding the robustness of the distance between two given nodes has a linear time complexity. This is counterintuitive, because the diameter consists of the maximum distance over all pairs of nodes, thus one may expect that the robustness of the diameter reduces to testing the robustness of pairwise distances. On the technical side, the difficulty of the diameter is established through a reduction from hamiltonian paths. The linear time algorithm for deciding robustness of the distance relies on a new characterization of two-terminal series-parallel graphs (TTSPs) in terms of excluded rooted minor, which may be of independent interest.

Cite as

Arnaud Casteigts, Timothée Corsini, Hervé Hocquard, and Arnaud Labourel. Robustness of Distances and Diameter in a Fragile Network. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 9:1-9:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{casteigts_et_al:LIPIcs.SAND.2022.9,
  author =	{Casteigts, Arnaud and Corsini, Timoth\'{e}e and Hocquard, Herv\'{e} and Labourel, Arnaud},
  title =	{{Robustness of Distances and Diameter in a Fragile Network}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.9},
  URN =		{urn:nbn:de:0030-drops-159514},
  doi =		{10.4230/LIPIcs.SAND.2022.9},
  annote =	{Keywords: Dynamic networks, Longest path, Series-parallel graphs, Rooted minors}
}
Document
Computing Outside the Box: Average Consensus over Dynamic Networks

Authors: Bernadette Charron-Bost and Patrick Lambein-Monette


Abstract
Networked systems of autonomous agents, and applications thereof, often rely on the control primitive of average consensus, where the agents are to compute the average of private initial values. To provide reliable services that are easy to deploy, average consensus should continue to operate when the network is subject to frequent and unpredictable change, and should mobilize few computational resources, so that deterministic, low powered, and anonymous agents can partake in the network. In this stringent adversarial context, we investigate the implementation of average consensus by distributed algorithms over networks with bidirectional, but potentially short-lived, communication links. Inspired by convex recurrence rules for multi-agent systems, and the Metropolis average consensus rule in particular, we design a deterministic distributed algorithm that achieves asymptotic average consensus, which we show to operate in polynomial time in a synchronous temporal model. The algorithm is easy to implement, has low space and computational complexity, and is fully distributed, requiring neither symmetry-breaking devices like unique identifiers, nor global control or knowledge of the network. In the fully decentralized model that we adopt, to our knowledge, no other distributed average consensus algorithm has a better temporal complexity. Our approach distinguishes itself from classical convex recurrence rules in that the agent’s values may sometimes leave their previous convex hull. As a consequence, our convergence bound requires a subtle analysis, despite the syntactic simplicity of our algorithm.

Cite as

Bernadette Charron-Bost and Patrick Lambein-Monette. Computing Outside the Box: Average Consensus over Dynamic Networks. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 10:1-10:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{charronbost_et_al:LIPIcs.SAND.2022.10,
  author =	{Charron-Bost, Bernadette and Lambein-Monette, Patrick},
  title =	{{Computing Outside the Box: Average Consensus over Dynamic Networks}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.10},
  URN =		{urn:nbn:de:0030-drops-159521},
  doi =		{10.4230/LIPIcs.SAND.2022.10},
  annote =	{Keywords: average consensus, dynamic networks, distributed algorithms, iterated averaging, Metropolis}
}
Document
Fast and Succinct Population Protocols for Presburger Arithmetic

Authors: Philipp Czerner, Roland Guttenberg, Martin Helfrich, and Javier Esparza


Abstract
In their 2006 seminal paper in Distributed Computing, Angluin et al. present a construction that, given any Presburger predicate as input, outputs a leaderless population protocol that decides the predicate. The protocol for a predicate of size m (when expressed as a Boolean combination of threshold and remainder predicates with coefficients in binary) runs in 𝒪(m ⋅ n² log n) expected number of interactions, which is almost optimal in n, the number of interacting agents. However, the number of states of the protocol is exponential in m. This is a problem for natural computing applications, where a state corresponds to a chemical species and it is difficult to implement protocols with many states. Blondin et al. described in STACS 2020 another construction that produces protocols with a polynomial number of states, but exponential expected number of interactions. We present a construction that produces protocols with 𝒪(m) states that run in expected 𝒪(m⁷ ⋅ n²) interactions, optimal in n, for all inputs of size Ω(m). For this, we introduce population computers, a carefully crafted generalization of population protocols easier to program, and show that our computers for Presburger predicates can be translated into fast and succinct population protocols.

Cite as

Philipp Czerner, Roland Guttenberg, Martin Helfrich, and Javier Esparza. Fast and Succinct Population Protocols for Presburger Arithmetic. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 11:1-11:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{czerner_et_al:LIPIcs.SAND.2022.11,
  author =	{Czerner, Philipp and Guttenberg, Roland and Helfrich, Martin and Esparza, Javier},
  title =	{{Fast and Succinct Population Protocols for Presburger Arithmetic}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.11},
  URN =		{urn:nbn:de:0030-drops-159535},
  doi =		{10.4230/LIPIcs.SAND.2022.11},
  annote =	{Keywords: population protocols, fast, succinct, population computers}
}
Document
Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems

Authors: Joshua J. Daymude, Andréa W. Richa, and Christian Scheideler


Abstract
Mutual exclusion is a classical problem in distributed computing that provides isolation among concurrent action executions that may require access to the same shared resources. Inspired by algorithmic research on distributed systems of weakly capable entities whose connections change over time, we address the local mutual exclusion problem that tasks each node with acquiring exclusive locks for itself and the maximal subset of its "persistent" neighbors that remain connected to it over the time interval of the lock request. Using the established time-varying graphs model to capture adversarial topological changes, we propose and rigorously analyze a local mutual exclusion algorithm for nodes that are anonymous and communicate via asynchronous message passing. The algorithm satisfies mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1) under both semi-synchronous and asynchronous concurrency. It requires 𝒪(Δ) memory per node and messages of size Θ(1), where Δ is the maximum number of connections per node. We conclude by describing how our algorithm can implement the pairwise interactions assumed by population protocols and the concurrency control operations assumed by the canonical amoebot model, demonstrating its utility in both passively and actively dynamic distributed systems.

Cite as

Joshua J. Daymude, Andréa W. Richa, and Christian Scheideler. Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 12:1-12:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{daymude_et_al:LIPIcs.SAND.2022.12,
  author =	{Daymude, Joshua J. and Richa, Andr\'{e}a W. and Scheideler, Christian},
  title =	{{Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.12},
  URN =		{urn:nbn:de:0030-drops-159545},
  doi =		{10.4230/LIPIcs.SAND.2022.12},
  annote =	{Keywords: Mutual exclusion, dynamic networks, message passing, concurrency}
}
Document
Dynamic Size Counting in Population Protocols

Authors: David Doty and Mahsa Eftekhari


Abstract
The population protocol model describes a network of anonymous agents that interact asynchronously in pairs chosen at random. Each agent starts in the same initial state s. We introduce the dynamic size counting problem: approximately counting the number of agents in the presence of an adversary who at any time can remove any number of agents or add any number of new agents in state s. A valid solution requires that after each addition/removal event, resulting in population size n, with high probability each agent "quickly" computes the same constant-factor estimate of the value log₂(n) (how quickly is called the convergence time), which remains the output of every agent for as long as possible (the holding time). Since the adversary can remove agents, the holding time is necessarily finite: even after the adversary stops altering the population, it is impossible to stabilize to an output that never again changes. We first show that a protocol solves the dynamic size counting problem if and only if it solves the loosely-stabilizing counting problem: that of estimating log n in a fixed-size population, but where the adversary can initialize each agent in an arbitrary state, with the same convergence time and holding time. We then show a protocol solving the loosely-stabilizing counting problem with the following guarantees: if the population size is n, M is the largest initial estimate of log n, and s is the maximum integer initially stored in any field of the agents' memory, we have expected convergence time O(log n + log M), expected polynomial holding time, and expected memory usage of O(log²(s) + (log log n)²) bits. Interpreted as a dynamic size counting protocol, when changing from population size n_prev to n_next, the convergence time is O(log n_next + log log n_prev).

Cite as

David Doty and Mahsa Eftekhari. Dynamic Size Counting in Population Protocols. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 13:1-13:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{doty_et_al:LIPIcs.SAND.2022.13,
  author =	{Doty, David and Eftekhari, Mahsa},
  title =	{{Dynamic Size Counting in Population Protocols}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.13},
  URN =		{urn:nbn:de:0030-drops-159558},
  doi =		{10.4230/LIPIcs.SAND.2022.13},
  annote =	{Keywords: Loosely-stabilizing, population protocols, size counting}
}
Document
Simulating 3-Symbol Turing Machines with SIMD||DNA

Authors: David Doty and Aaron Ong


Abstract
SIMD||DNA [Wang et al., 2019] is a model of DNA strand displacement allowing parallel in-memory computation on DNA storage. We show how to simulate an arbitrary 3-symbol space-bounded Turing machine with a SIMD||DNA program, giving a more direct and efficient route to general-purpose information manipulation on DNA storage than the Rule 110 simulation of Wang, Chalk, and Soloveichik [Wang et al., 2019]. We also develop software (https://github.com/UC-Davis-molecular-computing/simd-dna) that can simulate SIMD||DNA programs and produce SVG figures.

Cite as

David Doty and Aaron Ong. Simulating 3-Symbol Turing Machines with SIMD||DNA. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 14:1-14:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{doty_et_al:LIPIcs.SAND.2022.14,
  author =	{Doty, David and Ong, Aaron},
  title =	{{Simulating 3-Symbol Turing Machines with SIMD||DNA}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.14},
  URN =		{urn:nbn:de:0030-drops-159568},
  doi =		{10.4230/LIPIcs.SAND.2022.14},
  annote =	{Keywords: DNA storage, strand displacement, parallel computation}
}
Document
Parameterized Temporal Exploration Problems

Authors: Thomas Erlebach and Jakob T. Spooner


Abstract
In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph 𝒢 admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the vertices. Formally, a temporal graph is a sequence 𝒢 = ⟨ G₁,..., G_L⟩ of graphs with V(G_t) = V(G) and E(G_t) ⊆ E(G) for all t ∈ [L] and some underlying graph G, and a temporal walk is a time-respecting sequence of edge-traversals. For the strict variant, in which edges must be traversed in strictly increasing timesteps, we give FPT algorithms for the problem of finding a temporal walk that visits a given set X of vertices, parameterized by |X|, and for the problem of finding a temporal walk that visits at least k distinct vertices in V, parameterized by k. For the non-strict variant, in which an arbitrary number of edges can be traversed in each timestep, we parameterize by the lifetime L of the input graph and provide an FPT algorithm for the temporal exploration problem. We also give additional FPT or W[2]-hardness results for further problem variants.

Cite as

Thomas Erlebach and Jakob T. Spooner. Parameterized Temporal Exploration Problems. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 15:1-15:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{erlebach_et_al:LIPIcs.SAND.2022.15,
  author =	{Erlebach, Thomas and Spooner, Jakob T.},
  title =	{{Parameterized Temporal Exploration Problems}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.15},
  URN =		{urn:nbn:de:0030-drops-159570},
  doi =		{10.4230/LIPIcs.SAND.2022.15},
  annote =	{Keywords: Temporal graphs, fixed-parameter tractability, parameterized complexity}
}
Document
Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring

Authors: Till Fluschnik and Pascal Kunz


Abstract
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can be 2-colored in a way that results in few changes between any two consecutive layers. This approach follows the framework of multistage problems that has received a growing amount of attention in recent years. We investigate the complexity of recognizing these graphs. We show that this problem is NP-hard even if there are only two layers or if only one change is allowed between consecutive layers. We consider the parameterized complexity of the problem with respect to several structural graph parameters, which we transfer from the static to the temporal setting in three different ways. Finally, we consider a version of the problem in which we only restrict the total number of changes throughout the lifetime of the graph. We show that this variant is fixed-parameter tractable with respect to the number of changes.

Cite as

Till Fluschnik and Pascal Kunz. Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 16:1-16:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{fluschnik_et_al:LIPIcs.SAND.2022.16,
  author =	{Fluschnik, Till and Kunz, Pascal},
  title =	{{Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.16},
  URN =		{urn:nbn:de:0030-drops-159587},
  doi =		{10.4230/LIPIcs.SAND.2022.16},
  annote =	{Keywords: structural parameters, NP-hardness, parameterized algorithms, multistage problems}
}
Document
Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Authors: Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken


Abstract
Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path.

Cite as

Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Temporal Connectivity: Coping with Foreseen and Unforeseen Delays. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 17:1-17:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{fuchsle_et_al:LIPIcs.SAND.2022.17,
  author =	{F\"{u}chsle, Eugen and Molter, Hendrik and Niedermeier, Rolf and Renken, Malte},
  title =	{{Temporal Connectivity: Coping with Foreseen and Unforeseen Delays}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.17},
  URN =		{urn:nbn:de:0030-drops-159598},
  doi =		{10.4230/LIPIcs.SAND.2022.17},
  annote =	{Keywords: Paths and walks in temporal graphs, static expansions of temporal graphs, two-player games, flow computations, dynamic programming, PSPACE-completeness}
}
Document
Fully Dynamic Four-Vertex Subgraph Counting

Authors: Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua


Abstract
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic amortized O(m^{1/2}) update time, and any other connected four-vertex subgraph which is not a clique in deterministic amortized update time O(m^{2/3}). Queries can be answered in constant time. We also study the query times for subgraphs containing an arbitrary edge that is supplied only with the query as well as the case where only subgraphs containing a vertex s that is fixed beforehand are considered. For length-3 paths, paws, 4-cycles, and diamonds our bounds match or are not far from (conditional) lower bounds: Based on the OMv conjecture we show that any dynamic algorithm that detects the existence of paws, diamonds, or 4-cycles or that counts length-3 paths takes update time Ω(m^{1/2-δ}). Additionally, for 4-cliques and all connected induced subgraphs, we show a lower bound of Ω(m^{1-δ}) for any small constant δ > 0 for the amortized update time, assuming the static combinatorial 4-clique conjecture holds. This shows that the O(m) algorithm by Eppstein et al. [David Eppstein et al., 2012] for these subgraphs cannot be improved by a polynomial factor.

Cite as

Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua. Fully Dynamic Four-Vertex Subgraph Counting. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 18:1-18:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.18,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Hua, Qi Cheng},
  title =	{{Fully Dynamic Four-Vertex Subgraph Counting}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.18},
  URN =		{urn:nbn:de:0030-drops-159608},
  doi =		{10.4230/LIPIcs.SAND.2022.18},
  annote =	{Keywords: Dynamic Graph Algorithms, Subgraph Counting, Motif Search}
}
Document
Temporal Unit Interval Independent Sets

Authors: Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier


Abstract
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. We introduce and investigate the Temporal Δ Independent Set problem, a temporal variant of the well known Independent Set problem. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a day if their time-intervals overlap on that day. This leads us to considering Temporal Δ Independent Set on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is unit interval. We present several hardness results for this problem, as well as two algorithms: The first is a constant-factor approximation algorithm for instances where τ, the total number of time steps (layers) of the temporal graph, and Δ, a parameter that allows us to model some tolerance in the conflicts, are constants. For the second result we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. We provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.

Cite as

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier. Temporal Unit Interval Independent Sets. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 19:1-19:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hermelin_et_al:LIPIcs.SAND.2022.19,
  author =	{Hermelin, Danny and Itzhaki, Yuval and Molter, Hendrik and Niedermeier, Rolf},
  title =	{{Temporal Unit Interval Independent Sets}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.19},
  URN =		{urn:nbn:de:0030-drops-159617},
  doi =		{10.4230/LIPIcs.SAND.2022.19},
  annote =	{Keywords: Temporal Graphs, Vertex Orderings, Order Preservation, Interval Graphs, Algorithms and Complexity}
}
Document
Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid

Authors: Ryonosuke Yamada and Yukiko Yamauchi


Abstract
We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules increases, the variety of actions that the MRS can perform increases. The search problem requires the MRS to find a target in a given finite field. Doi et al. (SSS 2018) demonstrate a necessary and sufficient number of modules for search in a finite 2D square grid. We consider search in a finite 3D cubic grid and investigate the effect of common knowledge. We consider three different settings. First, we show that three modules are necessary and sufficient when all modules are equipped with a common compass, i.e., they agree on the direction and orientation of the x, y, and z axes. Second, we show that four modules are necessary and sufficient when all modules agree on the direction and orientation of the vertical axis. Finally, we show that five modules are necessary and sufficient when all modules are not equipped with a common compass. Our results show that the shapes of the MRS in the 3D cubic grid have richer structure than those in the 2D square grid.

Cite as

Ryonosuke Yamada and Yukiko Yamauchi. Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 20:1-20:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{yamada_et_al:LIPIcs.SAND.2022.20,
  author =	{Yamada, Ryonosuke and Yamauchi, Yukiko},
  title =	{{Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.20},
  URN =		{urn:nbn:de:0030-drops-159626},
  doi =		{10.4230/LIPIcs.SAND.2022.20},
  annote =	{Keywords: Distributed system, metamorphic robotic system, search, and 3D cubic grid}
}
Document
Brief Announcement
Brief Announcement: Cooperative Guarding in Polygons with Holes

Authors: John Augustine and Srikkanth Ramachandran


Abstract
We study the Cooperative Guarding problem for polygons with holes in a mobile multi-agents setting. Given a set of agents, initially deployed at a point in a polygon with n vertices and h holes, we require the agents to collaboratively explore and position themselves in such a way that every point in the polygon is visible to at least one agent and that the set of agents are visibly connected. We study the problem under two models of computation, one in which the agents can compute exact distances and angles between two points in its visibility, and one in which agents can only compare distances and angles. In the stronger model, we provide a deterministic O(n) round algorithm to compute such a cooperative guard set while not requiring more than (n + h)/2 agents and O(log n) bits of persistent memory per agent. In the weaker model, we provide an O(n⁴) round algorithm, that does not require more than (n+2h)/2 agents.

Cite as

John Augustine and Srikkanth Ramachandran. Brief Announcement: Cooperative Guarding in Polygons with Holes. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 21:1-21:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{augustine_et_al:LIPIcs.SAND.2022.21,
  author =	{Augustine, John and Ramachandran, Srikkanth},
  title =	{{Brief Announcement: Cooperative Guarding in Polygons with Holes}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{21:1--21:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.21},
  URN =		{urn:nbn:de:0030-drops-159636},
  doi =		{10.4230/LIPIcs.SAND.2022.21},
  annote =	{Keywords: Mobile Agents, Art Gallery Problem, Cooperative Guarding}
}
Document
Brief Announcement
Brief Announcement: The Temporal Firefighter Problem

Authors: Samuel D. Hand, Jessica Enright, and Kitty Meeks


Abstract
The Firefighter problem asks how many vertices can be saved from a fire spreading over the vertices of a graph. At timestep 0 a vertex begins burning, then on each subsequent timestep a non-burning vertex is chosen to be defended, and the fire then spreads to all undefended vertices that it neighbours. The problem is NP-Complete on arbitrary graphs, however existing work has found several graph classes for which there are polynomial time solutions. We introduce Temporal Firefighter, an extension of Firefighter to temporal graphs. We show that Temporal Firefighter is also NP-Complete, and remains so on all but one of the underlying classes of graphs on which Firefighter is known to have a polynomial-time solution. This motivates us to explore restrictions on the temporal structure of the graph, and we find that Temporal Firefighter is fixed parameter tractable with respect to the temporal graph parameter vertex-interval-membership-width.

Cite as

Samuel D. Hand, Jessica Enright, and Kitty Meeks. Brief Announcement: The Temporal Firefighter Problem. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 22:1-22:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hand_et_al:LIPIcs.SAND.2022.22,
  author =	{Hand, Samuel D. and Enright, Jessica and Meeks, Kitty},
  title =	{{Brief Announcement: The Temporal Firefighter Problem}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{22:1--22:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.22},
  URN =		{urn:nbn:de:0030-drops-159644},
  doi =		{10.4230/LIPIcs.SAND.2022.22},
  annote =	{Keywords: Temporal graphs, Spreading processes, Parameterised complexity}
}
Document
Brief Announcement
Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model

Authors: Irina Kostitsyna, Christian Scheideler, and Daniel Warner


Abstract
The amoebot model is a distributed computing model of programmable matter. It envisions programmable matter as a collection of computational units called amoebots or particles that utilize local interactions to achieve tasks of coordination, movement and conformation. In the geometric amoebot model the particles operate on a hexagonal tessellation of the plane. Within this model, numerous problems such as leader election, shape formation or object coating have been studied. One area that has not received much attention so far, but is highly relevant for a practical implementation of programmable matter, is fault tolerance. The existing literature on that aspect allows particles to crash but assumes that crashed particles do not recover. We propose a new model in which a crash causes the memory of a particle to be reset and a crashed particle can detect that it has crashed and try to recover using its local information and communication capabilities. We propose an algorithm that solves the hexagon shape formation problem in our model if a finite number of crashes occur and a designated leader particle does not fail. At the heart of our solution lies a fault-tolerant implementation of the spanning forest primitive, which, since other algorithms in the amoebot model also make use of it, is also of general interest.

Cite as

Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 23:1-23:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{kostitsyna_et_al:LIPIcs.SAND.2022.23,
  author =	{Kostitsyna, Irina and Scheideler, Christian and Warner, Daniel},
  title =	{{Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{23:1--23:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.23},
  URN =		{urn:nbn:de:0030-drops-159656},
  doi =		{10.4230/LIPIcs.SAND.2022.23},
  annote =	{Keywords: Programmable matter, Geometric amoebot model, Fault tolerance, Shape formation}
}
Document
Brief Announcement
Brief Announcement: Barrier-1 Reachability for Thermodynamic Binding Networks Is PSPACE-Complete

Authors: Austin Luchsinger


Abstract
Chemical and molecular systems exist in a world between kinetics and thermodynamics. Engineers of such systems often design them to perform computation solely by following particular kinetic pathways. That is, just like silicon computation, these systems are intentionally designed to run contrary to the natural thermodynamic driving forces of the system. The thermodynamic binding networks (TBN) model is a relatively new model that is particularly well-equipped to investigate this dichotomy between kinetics and thermodynamics. The kinetic TBN model uses reconfiguration energy barriers to inform kinetic pathways. This work shows that deciding if two TBN configurations have a barrier-1 pathway between them is PSPACE-complete. This result comes via a reduction from nondeterministic constraint logic (NCL).

Cite as

Austin Luchsinger. Brief Announcement: Barrier-1 Reachability for Thermodynamic Binding Networks Is PSPACE-Complete. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 24:1-24:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{luchsinger:LIPIcs.SAND.2022.24,
  author =	{Luchsinger, Austin},
  title =	{{Brief Announcement: Barrier-1 Reachability for Thermodynamic Binding Networks Is PSPACE-Complete}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{24:1--24:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.24},
  URN =		{urn:nbn:de:0030-drops-159664},
  doi =		{10.4230/LIPIcs.SAND.2022.24},
  annote =	{Keywords: Thermodynamic Binding Networks, Nondeterministic Constraint Logic, NP-complete, PSPACE-complete}
}

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