LIPIcs, Volume 292

3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)



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Event

SAND 2024, June 5-7, 2024, Patras, Greece

Editors

Arnaud Casteigts
  • University of Geneva, Switzerland
Fabian Kuhn
  • University of Freiburg, Germany

Publication Details

  • published at: 2024-05-31
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
  • ISBN: 978-3-95977-315-7
  • DBLP: db/conf/sand/sand2024

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Document
Complete Volume
LIPIcs, Volume 292, SAND 2024, Complete Volume

Authors: Arnaud Casteigts and Fabian Kuhn


Abstract
LIPIcs, Volume 292, SAND 2024, Complete Volume

Cite as

3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 1-374, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Proceedings{casteigts_et_al:LIPIcs.SAND.2024,
  title =	{{LIPIcs, Volume 292, SAND 2024, Complete Volume}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{1--374},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024},
  URN =		{urn:nbn:de:0030-drops-198779},
  doi =		{10.4230/LIPIcs.SAND.2024},
  annote =	{Keywords: LIPIcs, Volume 292, SAND 2024, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Arnaud Casteigts and Fabian Kuhn


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

Cite as

3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{casteigts_et_al:LIPIcs.SAND.2024.0,
  author =	{Casteigts, Arnaud and Kuhn, Fabian},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.0},
  URN =		{urn:nbn:de:0030-drops-198783},
  doi =		{10.4230/LIPIcs.SAND.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Exploration and Rendezvous in Temporal Graphs (Invited Talk)

Authors: Thomas Erlebach


Abstract
Given a temporal graph 𝒢 and a start vertex v in 𝒢, the temporal exploration problem (TEXP) is the problem of determining a temporal walk that starts at v and visits all vertices of 𝒢, with the objective of minimizing the time when the last unvisited vertex is reached. Studies have investigated the (parameterized) complexity and approximability of TEXP and the worst-case number of time steps required to complete an exploration. While many upper and lower bounds have been obtained for different settings, there are still some large gaps that pose interesting open problems. In this talk, we will give an overview of known results and techniques as well as open problems. Furthermore, we will discuss recent results (from joint work with Konstantinos Dogeas, Frank Kammer, Johannes Meintrup, and William K. Moses Jr) about exploiting symmetries in temporal graphs to get faster exploration. We view the number of automorphism orbits of the temporal graph as a new parameter, termed the orbit number, that may also be useful in other contexts. Finally, we show how a subroutine for quickly exploring a single orbit of the graph can be exploited to solve a certain rendezvous problem with two agents using a near-linear number of time steps in every always-connected temporal graph.

Cite as

Thomas Erlebach. Exploration and Rendezvous in Temporal Graphs (Invited Talk). In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{erlebach:LIPIcs.SAND.2024.1,
  author =	{Erlebach, Thomas},
  title =	{{Exploration and Rendezvous in Temporal Graphs}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.1},
  URN =		{urn:nbn:de:0030-drops-198797},
  doi =		{10.4230/LIPIcs.SAND.2024.1},
  annote =	{Keywords: Dynamic graphs, parameterized algorithms, orbit number}
}
Document
Invited Talk
Distributed Computation with Bacteria (Invited Talk)

Authors: Thomas Nowak


Abstract
Computing via synthetically engineered bacteria is a vibrant and active field with numerous applications in bio-production, bio-sensing, and medicine. Motivated by the lack of robustness and by resource limitation inside single cells, distributed approaches with communication among bacteria have recently gained in interest. In this talk, we describe the most important distributed approaches to synthetic biology with bacteria and discuss the crucial task of mathematical modeling of these systems. A particular problem is that of population growth happening concurrently, and possibly interfering, with the desired bio-computation. Specifically, we present a fast protocol in systems with continuous population growth for the majority consensus problem and prove that it correctly identifies the initial majority among two inputs with high probability. We also present a fast protocol that correctly computes the NAND of two inputs with high probability. By combining NAND gates with the majority consensus protocol as an amplifier, it is possible to compute arbitrary Boolean functions. The proposed protocols help set the stage for bio-engineered distributed computation that directly addresses continuous stochastic population growth. Own work presented in this talk is mostly based on joint work with Da-Jung Cho, Matthias Függer, Corbin Hopper, Manish Kushwaha, and Quentin Soubeyran.

Cite as

Thomas Nowak. Distributed Computation with Bacteria (Invited Talk). In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{nowak:LIPIcs.SAND.2024.2,
  author =	{Nowak, Thomas},
  title =	{{Distributed Computation with Bacteria}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.2},
  URN =		{urn:nbn:de:0030-drops-198807},
  doi =		{10.4230/LIPIcs.SAND.2024.2},
  annote =	{Keywords: Microbiological circuits, chemical reaction networks, birth-death processes}
}
Document
Invited Talk
Algorithmic Programmable Matter: From Local Markov Chains to "Dumb" Robots (Invited Talk)

Authors: Andréa Werneck Richa


Abstract
Many programmable matter systems have been developed, including modular and swarm robotics, synthetic biology, DNA tiling, and smart materials. We describe programmable matter as an abstract collection of simple computational elements (particles) with limited memory that each execute distributed, local algorithms to self-organize and solve system-wide problems, such as movement, reconfiguration, and coordination. Self-organizing particle systems (SOPS) have many interesting potential applications like coating objects for monitoring and repair purposes, and forming nano-scale devices for surgery and molecular-scale electronic structures. We describe some of our work on the algorithmic foundations of programmable matter, investigating how macro-scale system behaviors can naturally emerge from local micro-behaviors by individual particles: We utilize tools from statistical physics and Markov chain analysis to translate Markov chains defined at a system level into distributed, local algorithms for SOPS that drive the desired emergent collective behavior for the problems of compression, separation, and foraging, among others. We further establish the notion of algorithmic matter, where we leverage standard binary computation, as well as physical characteristics of the robots and interactions with the environment in order to implement our micro-level algorithms in actual testbeds composed of robots that are not capable of any standard computation. We conclude by addressing full concurrency and asynchrony in SOPS. This is joint work with Dana Randall and Dan Goldman (Georgia Tech), Michael Strano (MIT), Todd Murphey (Northwestern), Josh Daymude (Arizona State University), Sarah Cannon (Claremont McKenna), Christian Scheideler (University of Paderborn) and their research labs.

Cite as

Andréa Werneck Richa. Algorithmic Programmable Matter: From Local Markov Chains to "Dumb" Robots (Invited Talk). In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{richa:LIPIcs.SAND.2024.3,
  author =	{Richa, Andr\'{e}a Werneck},
  title =	{{Algorithmic Programmable Matter: From Local Markov Chains to "Dumb" Robots}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.3},
  URN =		{urn:nbn:de:0030-drops-198811},
  doi =		{10.4230/LIPIcs.SAND.2024.3},
  annote =	{Keywords: Programmable matter, Self-organizing particle systems, Biologically-inspired distributed algorithms, Local Markov chains, Emergent collective behavior}
}
Document
Harmonious Colourings of Temporal Matchings

Authors: Duncan Adamson


Abstract
Graph colouring is a fundamental problem in computer science, with a large body of research dedicated to both the general colouring problem and restricted cases. Harmonious colourings are one such restriction, where each edge must contain a globally unique pair of colours, i.e. if an edge connects a vertex coloured x with a vertex coloured y, then no other pair of connected vertices can be coloured x and y. Finding such a colouring in the traditional graph setting is known to be NP-hard, even in trees. This paper considers the generalisation of harmonious colourings to Temporal Graphs, specifically (k,t)-Temporal matchings, a class of temporal graphs where the underlying graph is a matching (a collection of disconnected components containing pairs of vertices), each edge can appear in at most t timesteps, and each timestep can contain at most k other edges. We provide a complete overview of the complexity landscape of finding temporal harmonious colourings for (k,t)-matchings. We show that finding a Temporal Harmonious Colouring, a colouring that is harmonious in each timestep, is NP-hard for (k,t)-Temporal Matchings when k ≥ 4, t ≥ 2, or when k ≥ 2 and t ≥ 3. We further show that this problem is inapproximable for t ≥ 2 and an unbounded value of k, and that the problem of determining the temporal harmonious chromatic number of a (2,3)-temporal matching can be determined in linear time. Finally, we strengthen this result by a set of upper and lower bounds of the temporal harmonious chromatic number both for individual temporal matchings and for the class of (k, t)-temporal matchings.

Cite as

Duncan Adamson. Harmonious Colourings of Temporal Matchings. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 4:1-4:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{adamson:LIPIcs.SAND.2024.4,
  author =	{Adamson, Duncan},
  title =	{{Harmonious Colourings of Temporal Matchings}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{4:1--4:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.4},
  URN =		{urn:nbn:de:0030-drops-198823},
  doi =		{10.4230/LIPIcs.SAND.2024.4},
  annote =	{Keywords: Temporal Graphs, Harmonious Colouring, NP-Completeness}
}
Document
Fault-Tolerant Distributed Directories

Authors: Judith Beestermöller, Costas Busch, and Roger Wattenhofer


Abstract
Many fundamental distributed computing problems require coordinated access to a shared resource. A distributed directory is an overlay data structure on an asynchronous graph G that helps to access a shared token t. The directory supports three basic operations: publish, to initialize the directory, lookup, to read the contents of the token, and move, to get exclusive update access to the token. There are known directory schemes that achieve message complexity within polylog factors of the optimal cost with respect to the number of nodes n and the diameter D of G. Motivated by fault-tolerant distributed computing implementations, we consider the impact of edge failures on distributed directories. We give a distributed directory overlay data structure that can tolerate edge failures without disrupting the directory operations. The directory can be repaired concurrently while it processes directory operations. We analyze the impact of the faults on the amortized cost of the three directory operations compared to the optimal cost. We show that f edges failures increase the amortized competitive ratio of the operations by at most factor f. We also analyze the message complexity to repair the overlay structure, in terms of the number of messages that are sent and the maximum distance a message traverses. For an edge failure, the repair mechanism uses messages of size 𝒪(log n) that traverse distance at most D', the graph diameter after the fault. To our knowledge, this is the first asymptotic analysis of a fault-tolerant distributed directory.

Cite as

Judith Beestermöller, Costas Busch, and Roger Wattenhofer. Fault-Tolerant Distributed Directories. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{beestermoller_et_al:LIPIcs.SAND.2024.5,
  author =	{Beesterm\"{o}ller, Judith and Busch, Costas and Wattenhofer, Roger},
  title =	{{Fault-Tolerant Distributed Directories}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.5},
  URN =		{urn:nbn:de:0030-drops-198833},
  doi =		{10.4230/LIPIcs.SAND.2024.5},
  annote =	{Keywords: distributed directory, sparse partition, fault tolerance, message complexity, path dilation}
}
Document
Black Hole Search in Dynamic Tori

Authors: Adri Bhattacharya, Giuseppe F. Italiano, and Partha Sarathi Mandal


Abstract
We investigate the black hole search problem using a set of mobile agents in a dynamic torus. A black hole is defined as a dangerous stationary node that has the capability to destroy any number of incoming agents without leaving any trace of its existence. A torus of size n× m (3 ≤ n ≤ m) is a collection of n row rings and m column rings, and the dynamicity is such that each ring is considered to be 1-interval connected, i.e., in other words at most one edge can be missing from each ring at any round. The parameters which define the efficiency of any black hole search algorithm are: the number of agents and the number of rounds (or time) for termination. We consider two initial configurations of mobile agents: first, the agents are co-located, second, the agents are scattered. In each case, we establish lower and upper bounds on the number of agents and on the amount of time required to solve the black hole search problem.

Cite as

Adri Bhattacharya, Giuseppe F. Italiano, and Partha Sarathi Mandal. Black Hole Search in Dynamic Tori. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bhattacharya_et_al:LIPIcs.SAND.2024.6,
  author =	{Bhattacharya, Adri and Italiano, Giuseppe F. and Mandal, Partha Sarathi},
  title =	{{Black Hole Search in Dynamic Tori}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.6},
  URN =		{urn:nbn:de:0030-drops-198840},
  doi =		{10.4230/LIPIcs.SAND.2024.6},
  annote =	{Keywords: Black Hole Search, Time Varying Graphs, Dynamic Torus, Distributed Algorithms, Mobile Agents}
}
Document
Online Space-Time Travel Planning in Dynamic Graphs

Authors: Quentin Bramas, Jean-Romain Luttringer, and Sébastien Tixeuil


Abstract
We study the problem of traveling in an unknown dynamic graph, to reach a destination with minimum latency. At each step of the execution, an agent can decide to move to a neighboring node if an edge exists at this time instant, wait at the current node in the hope that other links will appear in the future, or move backward in time using an expensive time travel device. A travel that makes use of backward time travel is called a space-time travel. Our aim is to arrive at the destination with zero delay, which always requires the use of backward time travel if no path exists to the destination during the first time instant. Finding an optimal space-time travel is polynomial when the agent knows the entire dynamic graph (including the future edges), even with additional constraints. However, we consider in this paper that the agent discovers the dynamic graph while it is exploring it, in an online manner. In this paper, we propose two models that define how an agent learns new knowledge about the dynamic graph during the execution of its protocol: the T-online model, where the agent reaching time t learns about the entire past of the network until t (even nodes not yet visited), and the S-online model, where the agent learns about the past and future about the current node he is located at. We present an algorithm with an optimal competitive ratio of 2 for the T-online model. In the S-online model, we prove a lower bound of 2/3n-7/4 and an upper bound of 2n-3 on the optimal competitive ratio when the cost function is linear.

Cite as

Quentin Bramas, Jean-Romain Luttringer, and Sébastien Tixeuil. Online Space-Time Travel Planning in Dynamic Graphs. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bramas_et_al:LIPIcs.SAND.2024.7,
  author =	{Bramas, Quentin and Luttringer, Jean-Romain and Tixeuil, S\'{e}bastien},
  title =	{{Online Space-Time Travel Planning in Dynamic Graphs}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.7},
  URN =		{urn:nbn:de:0030-drops-198854},
  doi =		{10.4230/LIPIcs.SAND.2024.7},
  annote =	{Keywords: Dynamic graphs, online algorithm, space-time travel, treasure hunt}
}
Document
On Inefficiently Connecting Temporal Networks

Authors: Esteban Christiann, Eric Sanlaville, and Jason Schoeters


Abstract
A temporal graph can be represented by a graph with an edge labelling, such that an edge is present in the network if and only if the edge is assigned the corresponding time label. A journey is a labelled path in a temporal graph such that labels on successive edges of the path are increasing, and if all vertices admit journeys to all other vertices, the temporal graph is temporally connected. A temporal spanner is a sublabelling of the temporal graph such that temporal connectivity is maintained. The study of temporal spanners has raised interest since the early 2000’s. Essentially two types of studies have been conducted: the positive side where families of temporal graphs are shown to (deterministically or stochastically) admit sparse temporal spanners, and the negative side where constructions of temporal graphs with no sparse spanners are of importance. Often such studies considered temporal graphs with happy or simple labellings, which associate exactly one label per edge. In this paper, we focus on the negative side and consider proper labellings, where multiple labels per edge are allowed. More precisely, we aim to construct dense temporally connected graphs such that all labels are necessary for temporal connectivity. Our contributions are multiple: we present exact or asymptotically tight results for basic graph families, which are then extended to larger graph families; an extension of an efficient temporal graph labelling generator; and overall denser labellings than previous work, whether it be global or local density.

Cite as

Esteban Christiann, Eric Sanlaville, and Jason Schoeters. On Inefficiently Connecting Temporal Networks. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{christiann_et_al:LIPIcs.SAND.2024.8,
  author =	{Christiann, Esteban and Sanlaville, Eric and Schoeters, Jason},
  title =	{{On Inefficiently Connecting Temporal Networks}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.8},
  URN =		{urn:nbn:de:0030-drops-198867},
  doi =		{10.4230/LIPIcs.SAND.2024.8},
  annote =	{Keywords: Network design principles, Network dynamics, Paths and connectivity problems, Branch-and-bound}
}
Document
All for One and One for All: An O(1)-Musketeers Universal Transformation for Rotating Robots

Authors: Matthew Connor, Othon Michail, and George Skretas


Abstract
In this paper, we settle the main open question of [Michail, Skretas, Spirakis, ICALP'17], asking what is the family of two-dimensional geometric shapes that can be transformed into each other by a sequence of rotation operations, none of which disconnects the shape. The model represents programmable matter systems consisting of interconnected modules that perform the minimal mechanical operation of 90° rotations around each other. The goal is to transform an initial shape of modules A into a target shape B. Under the necessary assumptions that the given shapes are connected and have identical colourings on a checkered colouring of the grid, and using a seed of only constant size, we prove that any pair of such shapes can be transformed into each other within an optimal O(n²) rotation operations none of which disconnects the shape.

Cite as

Matthew Connor, Othon Michail, and George Skretas. All for One and One for All: An O(1)-Musketeers Universal Transformation for Rotating Robots. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{connor_et_al:LIPIcs.SAND.2024.9,
  author =	{Connor, Matthew and Michail, Othon and Skretas, George},
  title =	{{All for One and One for All: An O(1)-Musketeers Universal Transformation for Rotating Robots}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.9},
  URN =		{urn:nbn:de:0030-drops-198874},
  doi =		{10.4230/LIPIcs.SAND.2024.9},
  annote =	{Keywords: programmable matter, universal transformation, reconfigurable robotics, shape formation, centralised algorithms}
}
Document
On the Complexity of Temporal Arborescence Reconfiguration

Authors: Riccardo Dondi and Manuel Lafond


Abstract
We analyze the complexity of Arborescence Reconfiguration on temporal digraphs (Temporal Arborescence Reconfiguration). The problem, given two temporal arborescences in a temporal digraph, asks for the minimum number of arc flips, i.e. arc exchanges, that result in a sequence of temporal arborescences that transforms one into the other. We analyze the complexity of the problem, taking into account also its approximation and parameterized complexity, even in restricted cases. First, we solve an open problem showing that Temporal Arborescence Reconfiguration is NP-hard for two timestamps. Then we show that even if the two temporal arborescences differ only by two arcs, then the problem is not approximable within factor bln|V(D)|, for any constant 0 < b < 1, where V(D) is the set of vertices of the temporal arborescences. Finally, we prove that Temporal Arborescence Reconfiguration is W[1]-hard when parameterized by the number of arc flips needed to transform one temporal arborescence into the other.

Cite as

Riccardo Dondi and Manuel Lafond. On the Complexity of Temporal Arborescence Reconfiguration. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{dondi_et_al:LIPIcs.SAND.2024.10,
  author =	{Dondi, Riccardo and Lafond, Manuel},
  title =	{{On the Complexity of Temporal Arborescence Reconfiguration}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.10},
  URN =		{urn:nbn:de:0030-drops-198888},
  doi =		{10.4230/LIPIcs.SAND.2024.10},
  annote =	{Keywords: Arborescence, Temporal Graphs, Graph Algorithms, Parameterized Complexity, Approximation Complexity}
}
Document
Partial Temporal Vertex Cover with Bounded Activity Intervals

Authors: Riccardo Dondi, Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, and Alessandra Tappini


Abstract
Different variants of Vertex Cover have recently garnered attention in the context of temporal graphs. One of these variants is motivated by the need to summarize timeline activities in social networks. Here, the activities of individual vertices, representing users, are characterized by time intervals. In this paper, we explore a scenario where the temporal span of each vertex’s activity interval is bounded by an integer 𝓁, and the objective is to maximize the number of (temporal) edges that are covered. We establish the APX-hardness of this problem and the NP-hardness of the corresponding decision problem, even under the restricted condition where the temporal domain comprises only two timestamps and each edge appears at most once. Subsequently, we delve into the parameterized complexity of the problem, offering two fixed-parameter algorithms parameterized by: (i) the number k of temporal edges covered by the solution, and (ii) the number h of temporal edges not covered by the solution. Finally, we present a polynomial-time approximation algorithm achieving a factor of 3/4.

Cite as

Riccardo Dondi, Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, and Alessandra Tappini. Partial Temporal Vertex Cover with Bounded Activity Intervals. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{dondi_et_al:LIPIcs.SAND.2024.11,
  author =	{Dondi, Riccardo and Montecchiani, Fabrizio and Ortali, Giacomo and Piselli, Tommaso and Tappini, Alessandra},
  title =	{{Partial Temporal Vertex Cover with Bounded Activity Intervals}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.11},
  URN =		{urn:nbn:de:0030-drops-198892},
  doi =		{10.4230/LIPIcs.SAND.2024.11},
  annote =	{Keywords: Temporal Graphs, Temporal Vertex Cover, Parameterized Complexity, Approximation Algorithms}
}
Document
Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization

Authors: Thomas Erlebach, Nils Morawietz, and Petra Wolf


Abstract
In the periodic temporal graph realization problem introduced by Klobas et al. [SAND '24] one is given a period Δ and an n× n matrix D of desired fastest travel times, and the task is to decide if there is a simple periodic temporal graph with period Δ such that the fastest travel time between any pair of vertices matches the one specified by D. We generalize the problem from simple temporal graphs to temporal graphs where each edge can appear up to 𝓁 times in each period, for some given integer 𝓁. For the resulting problem Multi-Label Periodic TGR, we show that it is fixed-parameter tractable for parameter n and for parameter vc+Δ, where vc is the vertex cover number of the underlying graph. We also show the existence of a polynomial kernel for parameter nu+d_max, where nu is the number of non-universal vertices of the underlying graph and d_max is the largest entry of D. Furthermore, we show that the problem is NP-hard for each 𝓁 ≥ 5, even if the underlying graph is a tree, a case that was known to be solvable in polynomial time if the task is to construct a simple periodic temporal graph, that is, if 𝓁 = 1.

Cite as

Thomas Erlebach, Nils Morawietz, and Petra Wolf. Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{erlebach_et_al:LIPIcs.SAND.2024.12,
  author =	{Erlebach, Thomas and Morawietz, Nils and Wolf, Petra},
  title =	{{Parameterized Algorithms for Multi-Label Periodic Temporal Graph Realization}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.12},
  URN =		{urn:nbn:de:0030-drops-198909},
  doi =		{10.4230/LIPIcs.SAND.2024.12},
  annote =	{Keywords: Fixed-Parameter Tractability, Almost-Clique, Kernelization, Dynamic Network, Temporal Graph}
}
Document
Computational Power of Opaque Robots

Authors: Caterina Feletti, Lucia Mambretti, Carlo Mereghetti, and Beatrice Palano


Abstract
In the field of distributed computing by robot swarms, the research comprehends manifold models where robots operate in the Euclidean plane through a sequence of look-compute-move cycles. Models under study differ for (i) the possibility of storing constant-size information, (ii) the possibility of communicating constant-size information, and (iii) the synchronization mode. By varying features (i,ii), we obtain the noted four base models: OBLOT (silent and oblivious robots), FSTA (silent and finite-state robots), FCOM (oblivious and finite-communication robots), and LUMI (finite-state and finite-communication robots). Combining each base model with the three main synchronization modes (fully synchronous, semi-synchronous, and asynchronous), we obtain the well-known 12 models. Extensive research has studied their computational power, proving the hierarchical relations between different models. However, only transparent robots have been considered. In this work, we study the taxonomy of the 12 models considering collision-intolerant opaque robots. We present six witness problems that prove the majority of the computational relations between the 12 models. In particular, the last witness problem depicts a peculiar issue occurring in the case of obstructed visibility and asynchrony.

Cite as

Caterina Feletti, Lucia Mambretti, Carlo Mereghetti, and Beatrice Palano. Computational Power of Opaque Robots. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{feletti_et_al:LIPIcs.SAND.2024.13,
  author =	{Feletti, Caterina and Mambretti, Lucia and Mereghetti, Carlo and Palano, Beatrice},
  title =	{{Computational Power of Opaque Robots}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.13},
  URN =		{urn:nbn:de:0030-drops-198913},
  doi =		{10.4230/LIPIcs.SAND.2024.13},
  annote =	{Keywords: Mobile robots, Look-Compute-Move, Computational complexity, Opaque robots, Distributed computing, Obstructed visibility, Collision intolerance}
}
Document
Forming Large Patterns with Local Robots in the OBLOT Model

Authors: Christopher Hahn, Jonas Harbig, and Peter Kling


Abstract
In the arbitrary pattern formation problem, n autonomous, mobile robots must form an arbitrary pattern P ⊆ R². The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form P under a natural symmetry condition if robots have no memory but an unlimited viewing range [Masafumi Yamashita and Ichiro Suzuki, 2010] or if robots have a limited viewing range but memory [Yukiko Yamauchi and Masafumi Yamashita, 2013]. In the latter case, P is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that P can be formed under the same symmetry condition if the robots' initial diameter is ≤ 1. Our protocol partitions P into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while "drawing" P by dropping one robot per pattern coordinate.

Cite as

Christopher Hahn, Jonas Harbig, and Peter Kling. Forming Large Patterns with Local Robots in the OBLOT Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{hahn_et_al:LIPIcs.SAND.2024.14,
  author =	{Hahn, Christopher and Harbig, Jonas and Kling, Peter},
  title =	{{Forming Large Patterns with Local Robots in the OBLOT Model}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.14},
  URN =		{urn:nbn:de:0030-drops-198924},
  doi =		{10.4230/LIPIcs.SAND.2024.14},
  annote =	{Keywords: Swarm Algorithm, Swarm Robots, Distributed Algorithm, Pattern Formation, Limited Visibility, Oblivious}
}
Document
Efficient Shape Formation by 3D Hybrid Programmable Matter: An Algorithm for Low Diameter Intermediate Structures

Authors: Kristian Hinnenthal, David Liedtke, and Christian Scheideler


Abstract
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through pick-up, movement, and placement actions. The goal is to reconfigure a set of tiles into a specific shape termed an icicle. The icicle, identified as a dense, hole-free structure, is strategically chosen to function as an intermediate shape for more intricate shape formation tasks. It is designed for easy exploration by a finite state agent, enabling the identification of tiles that can be lifted without breaking connectivity. Compared to the line shape, the icicle presents distinct advantages, including a reduced diameter and the presence of multiple removable tiles. We propose an algorithm that transforms an arbitrary initially connected tile structure into an icicle in 𝒪(n³) steps, matching the runtime of the line formation algorithm from prior work. Our theoretical contribution is accompanied by an extensive experimental analysis, indicating that our algorithm decreases the diameter of tile structures on average.

Cite as

Kristian Hinnenthal, David Liedtke, and Christian Scheideler. Efficient Shape Formation by 3D Hybrid Programmable Matter: An Algorithm for Low Diameter Intermediate Structures. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{hinnenthal_et_al:LIPIcs.SAND.2024.15,
  author =	{Hinnenthal, Kristian and Liedtke, David and Scheideler, Christian},
  title =	{{Efficient Shape Formation by 3D Hybrid Programmable Matter: An Algorithm for Low Diameter Intermediate Structures}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.15},
  URN =		{urn:nbn:de:0030-drops-198930},
  doi =		{10.4230/LIPIcs.SAND.2024.15},
  annote =	{Keywords: Programmable Matter, Shape Formation, 3D Model, Finite Automaton}
}
Document
Temporal Graph Realization from Fastest Paths

Authors: Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis


Abstract
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an n × n matrix D and a Δ ∈ ℕ, the goal is to construct a Δ-periodic temporal graph with n vertices such that the duration of a fastest path from v_i to v_j is equal to D_{i,j}, or to decide that such a temporal graph does not exist. The variations of the problem on static graphs has been well studied and understood since the 1960’s (e.g. [Erdős and Gallai, 1960], [Hakimi and Yau, 1965]). As it turns out, the periodic temporal graph realization problem has a very different computational complexity behavior than its static (i. e., non-temporal) counterpart. First we show that the problem is NP-hard in general, but polynomial-time solvable if the so-called underlying graph is a tree. Building upon those results, we investigate its parameterized computational complexity with respect to structural parameters of the underlying static graph which measure the "tree-likeness". We prove a tight classification between such parameters that allow fixed-parameter tractability (FPT) and those which imply W[1]-hardness. We show that our problem is W[1]-hard when parameterized by the feedback vertex number (and therefore also any smaller parameter such as treewidth, degeneracy, and cliquewidth) of the underlying graph, while we show that it is in FPT when parameterized by the feedback edge number (and therefore also any larger parameter such as maximum leaf number) of the underlying graph.

Cite as

Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis. Temporal Graph Realization from Fastest Paths. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{klobas_et_al:LIPIcs.SAND.2024.16,
  author =	{Klobas, Nina and Mertzios, George B. and Molter, Hendrik and Spirakis, Paul G.},
  title =	{{Temporal Graph Realization from Fastest Paths}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.16},
  URN =		{urn:nbn:de:0030-drops-198945},
  doi =		{10.4230/LIPIcs.SAND.2024.16},
  annote =	{Keywords: Temporal graph, periodic temporal labeling, fastest temporal path, graph realization, temporal connectivity, parameterized complexity}
}
Document
An Analysis of the Recurrence/Transience of Random Walks on Growing Trees and Hypercubes

Authors: Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai


Abstract
It is a celebrated fact that a simple random walk on an infinite k-ary tree for k ≥ 2 returns to the initial vertex at most finitely many times during infinitely many transitions; it is called transient. This work points out the fact that a simple random walk on an infinitely growing k-ary tree can return to the initial vertex infinitely many times, it is called recurrent, depending on the growing speed of the tree. Precisely, this paper is concerned with a simple specific model of a random walk on a growing graph (RWoGG), and shows a phase transition between the recurrence and transience of the random walk regarding the growing speed of the graph. To prove the phase transition, we develop a coupling argument, introducing the notion of less homesick as graph growing (LHaGG). We also show some other examples, including a random walk on {0,1}ⁿ with infinitely growing n, of the phase transition between the recurrence and transience. We remark that some graphs concerned in this paper have infinitely growing degrees.

Cite as

Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai. An Analysis of the Recurrence/Transience of Random Walks on Growing Trees and Hypercubes. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{kumamoto_et_al:LIPIcs.SAND.2024.17,
  author =	{Kumamoto, Shuma and Kijima, Shuji and Shirai, Tomoyuki},
  title =	{{An Analysis of the Recurrence/Transience of Random Walks on Growing Trees and Hypercubes}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.17},
  URN =		{urn:nbn:de:0030-drops-198955},
  doi =		{10.4230/LIPIcs.SAND.2024.17},
  annote =	{Keywords: Random walk, dynamic graph, recurrent, transient}
}
Document
Reconfiguration and Locomotion with Joint Movements in the Amoebot Model

Authors: Andreas Padalkin, Manish Kumar, and Christian Scheideler


Abstract
We are considering the geometric amoebot model where a set of n amoebots is placed on the triangular grid. An amoebot is able to send information to its neighbors, and to move via expansions and contractions. Since amoebots and information can only travel node by node, most problems have a natural lower bound of Ω(D) where D denotes the diameter of the structure. Inspired by the nervous and muscular system, Feldmann et al. have proposed the reconfigurable circuit extension and the joint movement extension of the amoebot model with the goal of breaking this lower bound. In the joint movement extension, the way amoebots move is altered. Amoebots become able to push and pull other amoebots. Feldmann et al. demonstrated the power of joint movements by transforming a line of amoebots into a rhombus within O(log n) rounds. However, they left the details of the extension open. The goal of this paper is therefore to formalize the joint movement extension. In order to provide a proof of concept for the extension, we consider two fundamental problems of modular robot systems: reconfiguration and locomotion. We approach these problems by defining meta-modules of rhombical and hexagonal shapes, respectively. The meta-modules are capable of movement primitives like sliding, rotating, and tunneling. This allows us to simulate reconfiguration algorithms of various modular robot systems. Finally, we construct three amoebot structures capable of locomotion by rolling, crawling, and walking, respectively.

Cite as

Andreas Padalkin, Manish Kumar, and Christian Scheideler. Reconfiguration and Locomotion with Joint Movements in the Amoebot Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{padalkin_et_al:LIPIcs.SAND.2024.18,
  author =	{Padalkin, Andreas and Kumar, Manish and Scheideler, Christian},
  title =	{{Reconfiguration and Locomotion with Joint Movements in the Amoebot Model}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.18},
  URN =		{urn:nbn:de:0030-drops-198963},
  doi =		{10.4230/LIPIcs.SAND.2024.18},
  annote =	{Keywords: programmable matter, modular robot system, reconfiguration, locomotion}
}
Document
Complexity of Boolean Automata Networks Under Block-Parallel Update Modes

Authors: Kévin Perrot, Sylvain Sené, and Léah Tapin


Abstract
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their 0-1 states according to local rules. The dynamics of the network is highly sensitive to update modes, i.e., to the schedule according to which the automata apply their local rule. A new family of update modes appeared recently, called block-parallel, which is dual to the well studied block-sequential. Although basic, it embeds the rich feature of update repetitions among a temporal updating period, allowing for atypical asymptotic behaviors. In this paper, we prove that it is able to breed complex computations, squashing almost all decision problems on the dynamics to the traditionally highest (for reachability questions) class PSPACE. Despite obtaining these complexity bounds for a broad set of local and global properties, we also highlight a surprising gap: bijectivity is still coNP.

Cite as

Kévin Perrot, Sylvain Sené, and Léah Tapin. Complexity of Boolean Automata Networks Under Block-Parallel Update Modes. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{perrot_et_al:LIPIcs.SAND.2024.19,
  author =	{Perrot, K\'{e}vin and Sen\'{e}, Sylvain and Tapin, L\'{e}ah},
  title =	{{Complexity of Boolean Automata Networks Under Block-Parallel Update Modes}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.19},
  URN =		{urn:nbn:de:0030-drops-198973},
  doi =		{10.4230/LIPIcs.SAND.2024.19},
  annote =	{Keywords: Boolean networks, finite dynamical systems, block-parallel update schedule}
}
Document
Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm

Authors: Avisek Sharma, Satakshi Ghosh, Pritam Goswami, and Buddhadeb Sau


Abstract
Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This problem has been extensively investigated in continuous and discrete scenarios, with this study focusing on the discrete variant. A set of robots is placed on the nodes of an infinite rectangular grid graph embedded in the euclidean plane. The movements of each robot is restricted to one of the four neighboring grid nodes from its current position. The robots are autonomous, anonymous, identical, and homogeneous, and operate Look-Compute-Move cycles. In this work, we adopt the classical OBLOT robot model, meaning the robots have no persistent memory or explicit communication methods, yet they possess full and unobstructed visibility. This work proposes an algorithm that solves the APF problem in a fully asynchronous scheduler assuming the initial configuration is asymmetric. The considered performance measures of the algorithm are space and number of moves required for the robots. The algorithm is asymptotically move-optimal. Here, we provide a definition of space complexity that takes the visibility issue into consideration. We observe an obvious lower bound 𝒟 of the space complexity and show that the proposed algorithm has the space complexity 𝒟+4. On comparing with previous related works, we show that this is the first proposed algorithm considering OBLOT robot model that is asymptotically move-optimal and has the least space complexity which is almost optimal.

Cite as

Avisek Sharma, Satakshi Ghosh, Pritam Goswami, and Buddhadeb Sau. Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{sharma_et_al:LIPIcs.SAND.2024.20,
  author =	{Sharma, Avisek and Ghosh, Satakshi and Goswami, Pritam and Sau, Buddhadeb},
  title =	{{Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.20},
  URN =		{urn:nbn:de:0030-drops-198989},
  doi =		{10.4230/LIPIcs.SAND.2024.20},
  annote =	{Keywords: Distributed algorithms, Oblivious robots, Optimal algorithms, Swarm robotics, Space optimization, and Rectangular grid}
}
Document
Gathering in Carrier Graphs: Meeting via Public Transportation System

Authors: Haozhi Zheng, Ryota Eguchi, Fukuhito Ooshita, and Michiko Inoue


Abstract
The gathering problem requires multiple mobile agents in a network to meet at a single location. This paper investigates the gathering problem in carrier graphs, a subclass of recurrence of edge class of time-varying graphs. By focusing on three subclasses of single carrier graphs - circular, simple, and arbitrary - we clarify the conditions under which the problem can be solved, considering prior knowledge endowed to agents and obtainable online information, such as the count and identifiers of agents or sites. We propose algorithms for solvable cases and analyze the complexities and we give proofs for the impossibility for unsolvable cases. We also consider general carrier graphs with multiple carriers and propose an algorithm for arbitrary carrier graphs. To the best of our knowledge, this is the first work that investigates the gathering problem in carrier graphs.

Cite as

Haozhi Zheng, Ryota Eguchi, Fukuhito Ooshita, and Michiko Inoue. Gathering in Carrier Graphs: Meeting via Public Transportation System. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{zheng_et_al:LIPIcs.SAND.2024.21,
  author =	{Zheng, Haozhi and Eguchi, Ryota and Ooshita, Fukuhito and Inoue, Michiko},
  title =	{{Gathering in Carrier Graphs: Meeting via Public Transportation System}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.21},
  URN =		{urn:nbn:de:0030-drops-198998},
  doi =		{10.4230/LIPIcs.SAND.2024.21},
  annote =	{Keywords: Gathering, Carrier Graph, Time-varying Graph, Mobile agent}
}
Document
Brief Announcement
Brief Announcement: Collision-Free Robot Scheduling

Authors: Duncan Adamson, Nathan Flaherty, Igor Potapov, and Paul G. Spirakis


Abstract
Robots are becoming an increasingly common part of scientific work within laboratory environments. In this paper, we investigate the problem of designing schedules for completing a set of tasks at fixed locations with multiple robots in a laboratory. We represent the laboratory as a graph with tasks placed on fixed vertices and robots represented as agents, with the constraint that no two robots may occupy the same vertex, or traverse the same edge, at the same time. Each schedule is partitioned into a set of timesteps, corresponding to a walk through the graph (allowing for a robot to wait at a vertex to complete a task), with each timestep taking time equal to the time for a robot to move from one vertex to another and each task taking some given number of timesteps during the completion of which a robot must stay at the vertex containing the task. The goal is to determine a set of schedules, with one schedule for each robot, minimising the number of timesteps taken by the schedule taking the greatest number of timesteps within the set of schedules. We show that the problem of finding a task-fulfilling schedule in at most L timesteps is NP-complete for many simple classes of graphs. Explicitly, we provide this result for complete graphs, bipartite graphs, star graphs, and planar graphs. Finally, we provide positive results for line graphs, showing that we can find an optimal set of schedules for k robots completing m tasks of equal length of a path of length n in O(kmn) time, and a k-approximation when the length of the tasks is unbounded.

Cite as

Duncan Adamson, Nathan Flaherty, Igor Potapov, and Paul G. Spirakis. Brief Announcement: Collision-Free Robot Scheduling. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 22:1-22:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{adamson_et_al:LIPIcs.SAND.2024.22,
  author =	{Adamson, Duncan and Flaherty, Nathan and Potapov, Igor and Spirakis, Paul G.},
  title =	{{Brief Announcement: Collision-Free Robot Scheduling}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{22:1--22:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.22},
  URN =		{urn:nbn:de:0030-drops-199004},
  doi =		{10.4230/LIPIcs.SAND.2024.22},
  annote =	{Keywords: Graph Exploration, Scheduling, NP-Completeness, Approximation Algorithms}
}
Document
Brief Announcement
Brief Announcement: On the Exponential Growth of Geometric Shapes

Authors: Nada Almalki, Siddharth Gupta, and Othon Michail


Abstract
We explore how geometric structures (or shapes) can be grown exponentially fast from a single node, through a sequence of centralized growth operations, and if collisions during growth are to be avoided. We identify a parameter k, representing the number of turning points within specific parts of a shape. We prove that, if edges can only be formed when generating new nodes and cannot be deleted, trees having O(k) turning points on every root-to-leaf path can be grown in O(klog n) time steps and spirals with O(log n) turning points can be grown in O(log n) time steps, n being the size of the final shape. For this case, we also show that the maximum number of turning points in a root-to-leaf path of a tree is a lower bound on the number of time steps to grow the tree and that there exists a class of paths such that any path in the class with Ω(k) turning points requires Ω(klog k) time steps to be grown. In the stronger model, where edges can be deleted and neighbors can be handed over to newly generated nodes, we obtain a universal algorithm: for any shape S it gives a process that grows S from a single node exponentially fast.

Cite as

Nada Almalki, Siddharth Gupta, and Othon Michail. Brief Announcement: On the Exponential Growth of Geometric Shapes. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 23:1-23:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{almalki_et_al:LIPIcs.SAND.2024.23,
  author =	{Almalki, Nada and Gupta, Siddharth and Michail, Othon},
  title =	{{Brief Announcement: On the Exponential Growth of Geometric Shapes}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{23:1--23:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.23},
  URN =		{urn:nbn:de:0030-drops-199015},
  doi =		{10.4230/LIPIcs.SAND.2024.23},
  annote =	{Keywords: centralized algorithm, growth process, collision, programmable matter}
}
Document
Brief Announcement
Brief Announcement: The Dynamic Steiner Tree Problem: Definitions, Complexity, Algorithms

Authors: Stefan Balev, Yoann Pigné, Éric Sanlaville, and Mathilde Vernet


Abstract
This note introduces an extension of the Steiner tree problem applied to dynamic graphs. It discusses its interest, studies its complexity and proposes an algorithm tested on generated and real data.

Cite as

Stefan Balev, Yoann Pigné, Éric Sanlaville, and Mathilde Vernet. Brief Announcement: The Dynamic Steiner Tree Problem: Definitions, Complexity, Algorithms. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 24:1-24:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{balev_et_al:LIPIcs.SAND.2024.24,
  author =	{Balev, Stefan and Pign\'{e}, Yoann and Sanlaville, \'{E}ric and Vernet, Mathilde},
  title =	{{Brief Announcement: The Dynamic Steiner Tree Problem: Definitions, Complexity, Algorithms}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{24:1--24:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.24},
  URN =		{urn:nbn:de:0030-drops-199026},
  doi =		{10.4230/LIPIcs.SAND.2024.24},
  annote =	{Keywords: Steiner Tree, Dynamic Graph, Complexity, experimental study}
}
Document
Brief Announcement
Brief Announcement: Crash-Tolerant Exploration of Trees by Energy Sharing Mobile Agents

Authors: Quentin Bramas, Toshimitsu Masuzawa, and Sébastien Tixeuil


Abstract
We consider the problem of graph exploration by energy sharing mobile agents that are subject to crash faults. More precisely, we consider a team of two agents where at most one of them may fail unpredictably, and the considered topology is that of acyclic graphs (i.e. trees). We consider both the asynchronous and the synchronous settings, and we provide necessary and sufficient conditions about the energy in two settings: line-shaped graphs, and general trees.

Cite as

Quentin Bramas, Toshimitsu Masuzawa, and Sébastien Tixeuil. Brief Announcement: Crash-Tolerant Exploration of Trees by Energy Sharing Mobile Agents. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 25:1-25:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bramas_et_al:LIPIcs.SAND.2024.25,
  author =	{Bramas, Quentin and Masuzawa, Toshimitsu and Tixeuil, S\'{e}bastien},
  title =	{{Brief Announcement: Crash-Tolerant Exploration of Trees by Energy Sharing Mobile Agents}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{25:1--25:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.25},
  URN =		{urn:nbn:de:0030-drops-199031},
  doi =		{10.4230/LIPIcs.SAND.2024.25},
  annote =	{Keywords: Mobile Agents, Distributed Algorithms, Energy sharing}
}
Document
Brief Announcement
Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them

Authors: Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin


Abstract
We consider geometric collision-detection problems for modular reconfigurable robots. Assuming the nodes (modules) are connected squares on a grid, we investigate the complexity of deciding whether collisions may occur, or can be avoided, if a set of expansion and contraction operations is executed. We study both discrete- and continuous-time models, and allow operations to be coupled into a single parallel group. Our algorithms to decide if a collision may occur run in O(n²log² n) time, O(n²) time, or O(nlog² n) time, depending on the presence and type of coupled operations, in a continuous-time model for a modular robot with n nodes. To decide if collisions can be avoided, we show that a very restricted version is already NP-complete in the discrete-time model, while the same problem is polynomial in the continuous-time model. A less restricted version is NP-hard in the continuous-time model.

Cite as

Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin. Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 26:1-26:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{gupta_et_al:LIPIcs.SAND.2024.26,
  author =	{Gupta, Siddharth and van Kreveld, Marc and Michail, Othon and Padalkin, Andreas},
  title =	{{Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{26:1--26:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.26},
  URN =		{urn:nbn:de:0030-drops-199044},
  doi =		{10.4230/LIPIcs.SAND.2024.26},
  annote =	{Keywords: Modular robots, Collision detection, Computational Geometry, Complexity}
}
Document
Brief Announcement
Brief Announcement: On the Existence of δ-Temporal Cliques in Random Simple Temporal Graphs

Authors: George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul G. Spirakis


Abstract
We consider random simple temporal graphs in which every edge of the complete graph K_n appears once within the time interval [0,1] independently and uniformly at random. Our main result is a sharp threshold on the size of any maximum δ-clique (namely a clique with edges appearing at most δ apart within [0,1]) in random instances of this model, for any constant δ. In particular, using the probabilistic method, we prove that the size of a maximum δ-clique is approximately (2 log n)/(log 1/δ) with high probability (whp). What seems surprising is that, even though the random simple temporal graph contains Θ(n²) overlapping δ-windows, which (when viewed separately) correspond to different random instances of the Erdős-Rényi random graphs model, the size of the maximum δ-clique in the former model and the maximum clique size of the latter are approximately the same. Furthermore, we show that the minimum interval containing a δ-clique is δ-o(δ) whp. We use this result to show that any polynomial time algorithm for δ-Temporal Clique is unlikely to have very large probability of success.

Cite as

George B. Mertzios, Sotiris Nikoletseas, Christoforos Raptopoulos, and Paul G. Spirakis. Brief Announcement: On the Existence of δ-Temporal Cliques in Random Simple Temporal Graphs. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 27:1-27:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{mertzios_et_al:LIPIcs.SAND.2024.27,
  author =	{Mertzios, George B. and Nikoletseas, Sotiris and Raptopoulos, Christoforos and Spirakis, Paul G.},
  title =	{{Brief Announcement: On the Existence of \delta-Temporal Cliques in Random Simple Temporal Graphs}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{27:1--27:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.27},
  URN =		{urn:nbn:de:0030-drops-199056},
  doi =		{10.4230/LIPIcs.SAND.2024.27},
  annote =	{Keywords: Simple random temporal graph, \delta-temporal clique, probabilistic method}
}

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