Volume
LIPIcs, Volume 330
4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Algorithmic Foundations of Dynamic Networks (SAND)
Event
SAND 2025, June 9-11, 2025, Liverpool, GBEditors
Publication Details
- published at: 2025-06-02
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-368-3
- DBLP: db/conf/sand/sand2025
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Document
Complete Volume
LIPIcs, Volume 330, SAND 2025, Complete Volume
Abstract
LIPIcs, Volume 330, SAND 2025, Complete Volume
Cite as
4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 1-342, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{meeks_et_al:LIPIcs.SAND.2025,
title = {{LIPIcs, Volume 330, SAND 2025, Complete Volume}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {1--342},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025},
URN = {urn:nbn:de:0030-drops-232691},
doi = {10.4230/LIPIcs.SAND.2025},
annote = {Keywords: LIPIcs, Volume 330, SAND 2025, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 0:i-0:viii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{meeks_et_al:LIPIcs.SAND.2025.0,
author = {Meeks, Kitty and Scheideler, Christian},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {0:i--0:viii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.0},
URN = {urn:nbn:de:0030-drops-232686},
doi = {10.4230/LIPIcs.SAND.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
The Expressive Power of Uniform Population Protocols with Logarithmic Space
Abstract
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n)∩𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly those predicates, whose unary encoding lies in NSPACE(f(n) log n).
Cite as
Philipp Czerner, Vincent Fischer, and Roland Guttenberg. The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{czerner_et_al:LIPIcs.SAND.2025.1,
author = {Czerner, Philipp and Fischer, Vincent and Guttenberg, Roland},
title = {{The Expressive Power of Uniform Population Protocols with Logarithmic Space}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {1:1--1:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.1},
URN = {urn:nbn:de:0030-drops-230540},
doi = {10.4230/LIPIcs.SAND.2025.1},
annote = {Keywords: Population Protocols, Uniform, Expressive Power}
}
Document
Dynamic Debt Swapping in Financial Networks
Abstract
A debt swap is an elementary edge swap in a directed, weighted graph, where two edges with the same weight swap their targets. Debt swaps are a natural and appealing operation in financial networks, in which nodes are banks and edges represent debt contracts. They can improve the clearing payments and the stability of these networks. However, their algorithmic properties are not well-understood.
We analyze the computational complexity of debt swapping. Our main interest lies in semi-positive swaps, in which no creditor strictly suffers and at least one strictly profits. These swaps lead to a Pareto-improvement in the entire network. We consider network optimization via sequences of v-improving debt swaps from which a given bank v strictly profits. For ranking-based clearing, we show that every sequence of semi-positive v-improving swaps has polynomial length. In contrast, for arbitrary v-improving swaps, the problem of reaching a network configuration that allows no further swaps is PLS-complete. We identify cases in which short sequences of semi-positive swaps exist even without the v-improving property.
Cite as
Henri Froese, Martin Hoefer, and Lisa Wilhelmi. Dynamic Debt Swapping in Financial Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{froese_et_al:LIPIcs.SAND.2025.2,
author = {Froese, Henri and Hoefer, Martin and Wilhelmi, Lisa},
title = {{Dynamic Debt Swapping in Financial Networks}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {2:1--2:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.2},
URN = {urn:nbn:de:0030-drops-230550},
doi = {10.4230/LIPIcs.SAND.2025.2},
annote = {Keywords: Debt Swap, Financial Networks, Local Search}
}
Document
Temporal Connectivity Augmentation
Abstract
Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More precisely, we tackle the problem of finding, among a set of proposed temporal edges, the smallest subset such that its addition makes the graph temporally connected (TCA). We study the complexity of this problem and variants, under restricted lifespan of the graph, i.e. the maximum time step in the graph. Our main result on TCA is that for any fixed lifespan at least 2, it is NP-complete in both the strict and non-strict setting. We additionally provide a set of restrictions in the non-strict setting which makes the problem solvable in polynomial time and design an algorithm achieving this complexity. Interestingly, we prove that the source variant (making a given vertex a source in the augmented graph) is as difficult as TCA. On the opposite, we prove that the version where a list of connectivity demands has to be satisfied is solvable in polynomial time, when the size of the list is fixed. Finally, we highlight a variant of the previous case for which even with two pairs the problem is already NP-hard.
Cite as
Thomas Bellitto, Jules Bouton Popper, and Bruno Escoffier. Temporal Connectivity Augmentation. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bellitto_et_al:LIPIcs.SAND.2025.3,
author = {Bellitto, Thomas and Popper, Jules Bouton and Escoffier, Bruno},
title = {{Temporal Connectivity Augmentation}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {3:1--3:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.3},
URN = {urn:nbn:de:0030-drops-230565},
doi = {10.4230/LIPIcs.SAND.2025.3},
annote = {Keywords: Temporal graph, temporal connectivity}
}
Document
On b-Matching and Fully-Dynamic Maximum k-Edge Coloring
Abstract
Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2.
We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant.
Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.
Cite as
Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-Matching and Fully-Dynamic Maximum k-Edge Coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{elhayek_et_al:LIPIcs.SAND.2025.4,
author = {El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika},
title = {{On b-Matching and Fully-Dynamic Maximum k-Edge Coloring}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {4:1--4:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.4},
URN = {urn:nbn:de:0030-drops-230571},
doi = {10.4230/LIPIcs.SAND.2025.4},
annote = {Keywords: dynamic algorithm, graph algorithm, matching, b-matching, edge coloring}
}
Document
Undecidability of the Emptiness Problem for Weak Models of Distributed Computing
Abstract
Esparza and Reiter have recently conducted a systematic comparative study of weak asynchronous models of distributed computing, in which a network of identical finite-state machines acts cooperatively to decide properties of the network’s graph. They introduced a distributed automata framework encompassing many different models, and proved that w.r.t. their expressive power (the graph properties they can decide) distributed automata collapse into seven equivalence classes. In this contribution, we turn our attention to the formal verification problem: Given a distributed automaton, does it decide a given graph property? We consider a fundamental instance of this question - the emptiness problem: Given a distributed automaton, does it accept any graph at all? Our main result is negative: the emptiness problem is undecidable for six of the seven equivalence classes, and trivially decidable for the remaining class.
Cite as
Flavio T. Principato, Javier Esparza, and Philipp Czerner. Undecidability of the Emptiness Problem for Weak Models of Distributed Computing. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{principato_et_al:LIPIcs.SAND.2025.5,
author = {Principato, Flavio T. and Esparza, Javier and Czerner, Philipp},
title = {{Undecidability of the Emptiness Problem for Weak Models of Distributed Computing}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {5:1--5:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.5},
URN = {urn:nbn:de:0030-drops-230582},
doi = {10.4230/LIPIcs.SAND.2025.5},
annote = {Keywords: Undecidability, Emptiness Problem, distributed Automata}
}
Document
Dismountability in Temporal Cliques Revisited
Abstract
A temporal graph is a graph whose edges are available only at certain points in time. It is temporally connected if the nodes can reach each other by paths that traverse the edges chronologically (temporal paths). Unlike static graphs, temporal graphs do not always admit small subsets of edges that preserve connectivity (temporal spanners) - there exist temporal graphs with Θ(n²) edges, all of which are critical. In the case of temporal cliques (the underlying graph is complete), spanners of size O(nlog n) are guaranteed. The original proof of this result by Casteigts et al. [ICALP 2019] combines a number of techniques, one of which is called dismountability. In a recent work, Angrick et al. [ESA 2024] simplified the proof and showed, among other things, that a one-sided version of dismountability can replace elegantly the second part of the proof.
In this paper, we revisit methodically the dismountability principle. We start by characterizing the structure that a temporal clique must have if it is non 1-hop dismountable, then neither 1-hop nor 2-hop (i.e. non {1,2}-hop) dismountable, and finally non {1,2,3}-hop dismountable. It turns out that if a clique is k-hop dismountable for any other k, then it must also be {1,2,3}-hop dismountable, thus no additional structure can be obtained beyond this point. Interestingly, excluding 1-hop and 2-hop dismountability is already sufficient for reducing the spanner problem from cliques to extremally matched bicliques, where the O(nlog n) result is subsequently obtained. Put together with the strategy of Angrick et al., this entire result can now be recovered using only dismountability. An interesting by-product of our analysis is that any minimal counter-example to the existence of 4n spanners must satisfy the properties of non {1,2,3}-hop dismountable cliques.
In the second part, we discuss further connections between dismountability and another technique called pivotability. In particular, we show that if a temporal clique is recursively k-hop dismountable, then it is also pivotable (and thus admits a 2n spanner, whatever k). We also study a family of labelings called full-range that forces both dismountability and pivotability. The latter gives some evidence that large lifetimes could be exploited more generally for the construction of spanners.
Cite as
Daniele Carnevale, Arnaud Casteigts, and Timothée Corsini. Dismountability in Temporal Cliques Revisited. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{carnevale_et_al:LIPIcs.SAND.2025.6,
author = {Carnevale, Daniele and Casteigts, Arnaud and Corsini, Timoth\'{e}e},
title = {{Dismountability in Temporal Cliques Revisited}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {6:1--6:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.6},
URN = {urn:nbn:de:0030-drops-230591},
doi = {10.4230/LIPIcs.SAND.2025.6},
annote = {Keywords: Dynamic networks, Temporal graphs, Reachability, Dismountability, Pivotability, Temporal spanners, Full-range graphs}
}
Document
Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs
Abstract
In train networks, carefully-chosen delays may be beneficial for certain passengers, who would otherwise miss some connection. Given a simple (directed or undirected) temporal graph and a set of passengers (each specifying a starting vertex, an ending vertex, and a desired arrival time), we ask whether it is possible to delay some of the edges of the temporal graph to realize all the passengers' demands. We call this problem DelayBetter (DB), and study it along with two variants: in δ-DelayBetter, each delay must be of at most δ; in (δ-)Path DB, passengers also fully specify the vertices they should visit on their journey. On the positive side, we give a polynomial-time algorithm for Path DB and δ-Path DB, and obtain as a corollary a polynomial-time algorithm for DB and δ-DB on trees. We also provide an fpt algorithm for both problems parameterized by the size of the graph’s Feedback Edge Set together with the number of passengers. On the negative side, we show NP-completeness of (1-)DB on bounded-degree temporal graphs even when the lifetime is 2, and of (10-)DB on bounded-degree planar temporal graphs of lifetime 19. Our results complement previous work studying reachability problems in temporal graphs with delaying operations. This is to our knowledge the first such problem in which the aim is to facilitate travel between specific points (as opposed to facilitating or impeding a broadcast from one or many sources).
Cite as
David C. Kutner and Anouk Sommer. Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kutner_et_al:LIPIcs.SAND.2025.7,
author = {Kutner, David C. and Sommer, Anouk},
title = {{Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {7:1--7:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.7},
URN = {urn:nbn:de:0030-drops-230604},
doi = {10.4230/LIPIcs.SAND.2025.7},
annote = {Keywords: Temporal Graphs, Computational Complexity, Delay Management, Train Networks}
}
Document
Matching and Edge Cover in Temporal Graphs
Abstract
Temporal graphs are a special class of graphs for which a temporal component is added to edges, that is, each edge possesses a set of times at which it is available and can be traversed. Many classical problems on graphs can be translated to temporal graphs, and the results may differ.
In this paper, we define the {Temporal Edge Cover} and {Temporal Matching} problems and show that they are NP-complete even when fixing the lifetime or when the underlying graph is a tree. We then describe two FPT algorithms, with parameters lifetime and treewidth, that solve the two problems. We also find lower bounds for the approximation of the two problems and give two approximation algorithms which match these bounds. Finally, we discuss the differences between the problems in the temporal and the static framework.
Cite as
Lapo Cioni, Riccardo Dondi, Andrea Marino, Jason Schoeters, and Ana Silva. Matching and Edge Cover in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{cioni_et_al:LIPIcs.SAND.2025.8,
author = {Cioni, Lapo and Dondi, Riccardo and Marino, Andrea and Schoeters, Jason and Silva, Ana},
title = {{Matching and Edge Cover in Temporal Graphs}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {8:1--8:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.8},
URN = {urn:nbn:de:0030-drops-230614},
doi = {10.4230/LIPIcs.SAND.2025.8},
annote = {Keywords: graphs, temporal graphs, edge cover, matching, parameterized algorithm, approximation algorithm}
}
Document
Spanner Enumeration for Temporal Graphs
Abstract
A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.
Cite as
Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kurita_et_al:LIPIcs.SAND.2025.9,
author = {Kurita, Kazuhiro and Marino, Andrea and Schoeters, Jason and Uno, Takeaki},
title = {{Spanner Enumeration for Temporal Graphs}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {9:1--9:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.9},
URN = {urn:nbn:de:0030-drops-230621},
doi = {10.4230/LIPIcs.SAND.2025.9},
annote = {Keywords: temporal graphs, temporal spanners, one-to-all connectivity, all-to-all connectivity enumeration, NP-completeness, Dual-hardness, binary partition tree, flashlight search, polynomial delay}
}
Document
Fault Detection and Identification by Autonomous Mobile Robots
Abstract
The Look-Compute-Move model (LCM) is adopted to study swarms of mobile robots that have to solve a given problem. Robots are generally assumed to be autonomous, indistinguishable, anonymous, homogeneous and to move on the Euclidean plane. Different LCM sub-models have been theorized to study different settings and their computational power. Notably, the literature has focused on four base models (i.e., OBLOT, FSTA, FCOM, LUMI) that differ in memory and communication capabilities, and in different synchronization modes (e.g., fully synchronous FSYNCH, semi-synchronous SSYNCH).
In this paper, we consider fault-prone models where robots can suffer from crash faults: each robot may irremediably stop working after an unpredictable time. We study the general Fault Detection (FD) problem which is solved by a swarm if it correctly detects whether a faulty robot exists in the swarm. The Fault Identification (FI) problem additionally requires identifying which robots are faulty. We consider 12 LCM sub-models (OBLOT, FSTA, FCOM, LUMI, combined with FSYNCH, SSYNCH, and the round-robin RROBIN) and we study the (im)possibility of designing reliable procedures to solve FD or FI. In particular, we propose three distributed algorithms so that a swarm can collectively solve FD under the models LUMI^FSYNCH, FCOM^FSYNCH, and LUMI^RROBIN.
Cite as
Stefano Clemente and Caterina Feletti. Fault Detection and Identification by Autonomous Mobile Robots. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{clemente_et_al:LIPIcs.SAND.2025.10,
author = {Clemente, Stefano and Feletti, Caterina},
title = {{Fault Detection and Identification by Autonomous Mobile Robots}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {10:1--10:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.10},
URN = {urn:nbn:de:0030-drops-230639},
doi = {10.4230/LIPIcs.SAND.2025.10},
annote = {Keywords: Autonomous mobile robots, Faulty robots, Look-Compute-Move, Fault detection, Fault identification, Round-robin}
}
Document
Hardness of Traversing Gadget Systems with Small Bandwidth
Abstract
The motion-planning-through-gadgets framework has enabled proofs of PSPACE-completeness for many motion-planning problems, ranging from swarm and modular robotics to DNA computing to video games. In this paper, we strengthen this framework to show that, for several useful gadgets and gadget families, motion planning remains PSPACE-complete even when gadgets are connected together into a graph of constant bandwidth (which implies constant pathwidth, treewidth, and cliquewidth). We then show how this result applies to several geometric/grid-based motion-planning problems, establishing PSPACE-completeness even when restricted to a rectangle/box where only one dimension is large (superconstant). On the positive side, we find one family of gadgets (DAG gadgets) for which motion planning is fixed-parameter tractable with respect to bandwidth.
Cite as
MIT Gadgets Group, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Markus Hecher, and Jayson Lynch. Hardness of Traversing Gadget Systems with Small Bandwidth. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{mitgadgetsgroup_et_al:LIPIcs.SAND.2025.11,
author = {MIT Gadgets Group and Demaine, Erik D. and Diomidova, Jenny and Gomez, Timothy and Hecher, Markus and Lynch, Jayson},
title = {{Hardness of Traversing Gadget Systems with Small Bandwidth}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {11:1--11:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.11},
URN = {urn:nbn:de:0030-drops-230648},
doi = {10.4230/LIPIcs.SAND.2025.11},
annote = {Keywords: Gadgets, Motion Planning, Parameterized Complexity, Hardness}
}
Document
Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs
Abstract
In the temporal graph exploration problem, an agent wishes to visit all the vertices of a temporal graph, moving at most one edge in every time step. In restless exploration, the agent is required to move in every step, and cannot wait at a vertex. We study the problem of restless exploration in vertex-permuted graphs, which are a class of temporal graphs in which the topology of the graph stays the same in every time step. In other words, in a vertex permuted temporal graph, in every step i, the graph G_i is isomorphic to the same base graph G. We give a precise characterization of graphs G such that restless exploration is possible in every vertex-permuted graph with base graph G. Our technique is based on an a characterization of networks in which there is an online distributed algorithm for restless token dissemination. Finally we describe some families of graphs in which restless exploration is always possible, and some in which it is not.
Cite as
Kamran Ayoubi and Lata Narayanan. Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ayoubi_et_al:LIPIcs.SAND.2025.12,
author = {Ayoubi, Kamran and Narayanan, Lata},
title = {{Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {12:1--12:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.12},
URN = {urn:nbn:de:0030-drops-230658},
doi = {10.4230/LIPIcs.SAND.2025.12},
annote = {Keywords: Temporal graphs, Vertex permuted graphs, Restless exploration, Periodic graphs, Token dissemination}
}
Document
Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents
Abstract
We study the Byzantine gathering problem involving k mobile agents with unique identifiers (IDs), f of which are Byzantine. These agents start the execution of a common algorithm from (possibly different) nodes in an n-node network, potentially starting at different times. Once started, the agents operate in synchronous rounds. We focus on weakly Byzantine environments, where Byzantine agents can behave arbitrarily but cannot falsify their IDs. The goal is for all non-Byzantine agents to eventually terminate at a single node simultaneously.
In this paper, we first prove two impossibility results: (1) for any number of non-Byzantine agents, no algorithm can solve this problem without global knowledge of the network size or the number of agents, and (2) no self-stabilizing algorithm exists if k ≤ 2f even with n, k, f, and the length Λ_g of the largest ID among IDs of non-Byzantine agents, where the self-stabilizing algorithm enables agents to gather starting from arbitrary (inconsistent) initial states. Next, based on these results, we introduce a perpetual gathering problem and propose a self-stabilizing algorithm for this problem. This problem requires that all non-Byzantine agents always be co-located from a certain time onwards. If the agents know Λ_g and upper bounds N, K, F on n, k, f, the proposed algorithm works in O(K⋅ F⋅ Λ_g⋅ X(N)) rounds, where X(n) is the time required to visit all nodes in a n-nodes network. Our results indicate that while no algorithm can solve the original self-stabilizing gathering problem for any k and f even with exact global knowledge of the network size and the number of agents, the self-stabilizing perpetual gathering problem can always be solved with just upper bounds on this knowledge.
Cite as
Jion Hirose, Ryota Eguchi, and Yuichi Sudo. Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hirose_et_al:LIPIcs.SAND.2025.13,
author = {Hirose, Jion and Eguchi, Ryota and Sudo, Yuichi},
title = {{Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {13:1--13:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.13},
URN = {urn:nbn:de:0030-drops-230662},
doi = {10.4230/LIPIcs.SAND.2025.13},
annote = {Keywords: Distributed algorithms, Byzantine environments, Gathering}
}
Document
Fractals in Seeded Tile Automata
Abstract
This work fully characterizes fractal generation in the seeded Tile Automata model (seeded TA), a model similar to the abstract Tile Assembly model (aTAM) with the added ability for adjacent tiles to change states. Under these assumptions, we first show that all discrete self-similar fractals (DSSFs) with feasible generators are strictly buildable at scale 1 and temperature 1 in seeded TA. We then show that these results imply the existence of a single seeded TA system Γ that can strictly build any DSSF infinitely at scale 1 and temperature 1.
Cite as
Asher Haun, Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, and Tim Wylie. Fractals in Seeded Tile Automata. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{haun_et_al:LIPIcs.SAND.2025.14,
author = {Haun, Asher and Knobel, Ryan and Salinas, Adrian and Santos, Ramiro and Schweller, Robert and Wylie, Tim},
title = {{Fractals in Seeded Tile Automata}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {14:1--14:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.14},
URN = {urn:nbn:de:0030-drops-230677},
doi = {10.4230/LIPIcs.SAND.2025.14},
annote = {Keywords: self-assembly, tile automata, fractals}
}
Document
On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks
Abstract
Algorithms for mutual exclusion aim to isolate potentially concurrent accesses to the same shared resources. Motivated by distributed computing research on programmable matter and population protocols where interactions among entities are often assumed to be isolated, Daymude, Richa, and Scheideler (SAND`22) introduced a variant of the local mutual exclusion problem that applies to arbitrary dynamic networks: each node, on issuing a lock request, must acquire exclusive locks on itself and all its persistent neighbors, i.e., the neighbors that remain connected to it over the duration of the lock request. Assuming adversarial edge dynamics, semi-synchronous or asynchronous concurrency, and anonymous nodes communicating via message passing, their randomized algorithm achieves mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1). However, they did not analyze their algorithm’s runtime. In this paper, we prove that any node will successfully lock itself and its persistent neighbors within 𝒪(nΔ³) open rounds of its lock request in expectation, where n is the number of nodes in the dynamic network, Δ is the maximum degree of the dynamic network, rounds are normalized to the execution time of the "slowest" node, and "closed" rounds when some persistent neighbors are already locked by another node are ignored (i.e., only "open" rounds are considered).
Cite as
Anya Chaturvedi, Joshua J. Daymude, and Andréa W. Richa. On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chaturvedi_et_al:LIPIcs.SAND.2025.15,
author = {Chaturvedi, Anya and Daymude, Joshua J. and Richa, Andr\'{e}a W.},
title = {{On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {15:1--15:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.15},
URN = {urn:nbn:de:0030-drops-230687},
doi = {10.4230/LIPIcs.SAND.2025.15},
annote = {Keywords: Mutual exclusion, dynamic networks, message passing, concurrency}
}
Document
Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions
Abstract
We study the Temporal Dominating Set problem, in which one asks whether a temporal graph 𝒢 = (G₁,… , G_T) given as a sequence of snapshot graphs, over the same vertex set V, has a set S of temporal vertices of size at most k such that each vertex v of V is dominated by some w ∈ S in the snapshot that contains w. Additionally, we consider Temporal Partial Dominating Set, where one asks whether at least t (and not necessarily all) vertices of V can be dominated by S and a further generalization in which the solution may only contain a bounded number of temporal vertices from each snapshot.
We analyze how the complexity of Temporal (Partial) Dominating Set is influenced by the maximum snapshot degree and the structure of the underlying graph, the graph with vertex set V and whose edge set is the union of all snapshot edge sets. For example, we obtain a complexity dichotomy for the maximum snapshot degree and we show that Temporal Partial Dominating Set is fixed-parameter tractable for tw+Δ, where tw and Δ denote the treewidth and the maximum degree of the underlying graph of 𝒢, respectively. We also show which of our results transfer to the well-studied Temporal Vertex Cover problem. For example, we show that Temporal Vertex Cover is also fixed-parameter tractable for tw+Δ which substantially extends the previously known polynomial-time algorithms for the case that the underlying graph is a path or cycle.
Cite as
Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{herrmann_et_al:LIPIcs.SAND.2025.16,
author = {Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
title = {{Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {16:1--16:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.16},
URN = {urn:nbn:de:0030-drops-230695},
doi = {10.4230/LIPIcs.SAND.2025.16},
annote = {Keywords: NP-hard problem, FPT-algorithm, Treewidth, Color coding}
}
Document
Brief Announcement
Brief Announcement: Broadcast via Mobile Agents in a Dynamic Network: Interplay of Graph Properties & Agents
Abstract
In this paper, we revisit the problem of Broadcast, introduced by Das, Giachoudis, Luccio, and Markou [OPODIS, 2020], where k+1 agents are initially placed on an n node dynamic graph, where 1 agent has a message that must be broadcast to the remaining k ignorant agents. The original paper studied the relationship between the number of agents needed to solve the problem and the edge density of the graph. The paper presented strong evidence that edge density of a graph, or the number of redundant edges within the graph, may be the correct graph property to accurately differentiate whether k = o(n) agents (low edge density) or k = Ω(n) agents (high edge density) are needed to solve the problem.
In this paper, we show that surprisingly, edge density is not in fact the differentiating property. The original paper presents graphs with edge density 1.1 ̅{6} that require Ω(n) agents, however, we construct graphs with edge density > 1.1 ̅{6} and develop an algorithm to solve the problem on those graphs using only o(n) agents. We further show that the relationship between edge density and number of agents is fairly weak by first constructing graphs with edge density tending to 1 from above that require Ω(n/f(n)) agents to solve, for any function f(n) → ∞ as n → ∞. We then construct an infinite family of graphs with edge density < ρ requiring exactly k ignorant agents to solve Broadcast, for any k > 0 and ρ > 1.
Finally, we investigate different versions of connectivity as possible properties determining the number of agents. We show that edge connectivity is not related to the number of agents: it is possible for a graph to have low (constant) edge connectivity but require a high (linear) number of agents to solve Broadcast. More generally, for any arbitrary λ, we construct a family of graphs on n nodes with edge connectivity (n-1)/λ requiring exactly k = n - 2 λ + 1 agents. On the other hand, we show vertex connectivity can impact the required number of agents: for any graph with vertex connectivity ≥ 3 and minimum degree δ, k ≥ δ - 1 agents are required to solve Broadcast. Finally, we show that for any graph containing a certain type of bond with m edges, Broadcast is unsolvable when k ≤ m-2.
Cite as
William K. Moses Jr., Amanda Redlich, and Frederick Stock. Brief Announcement: Broadcast via Mobile Agents in a Dynamic Network: Interplay of Graph Properties & Agents. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 17:1-17:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{mosesjr._et_al:LIPIcs.SAND.2025.17,
author = {Moses Jr., William K. and Redlich, Amanda and Stock, Frederick},
title = {{Brief Announcement: Broadcast via Mobile Agents in a Dynamic Network: Interplay of Graph Properties \& Agents}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {17:1--17:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.17},
URN = {urn:nbn:de:0030-drops-230708},
doi = {10.4230/LIPIcs.SAND.2025.17},
annote = {Keywords: Mobile agents, mobile robots, broadcast, dynamic graph, dynamic network}
}
Document
Brief Announcement
Brief Announcement: The Shortest Temporal Exploration Problem
Abstract
A temporal graph is a graph for which the edge set can change from one time step to the next. This paper considers undirected temporal graphs defined over L time steps and connected at each time step. We study the Shortest Temporal Exploration Problem (STEXP) that, given the evolution of the graph, asks for a temporal walk that starts at a given vertex, moves over at most one edge at each time step, visits all the vertices, takes at most L time steps and traverses the smallest number of edges. We prove that every constantly connected temporal graph with n vertices can be explored with O(n^{1.5}) edges traversed if L is O(n^{3.5}) time steps. This result improves the upper bound of O(n²) edges when L is Ω(n²). Moreover, we study the case where the graph has a diameter bounded by a parameter k at each time step and we prove that there exists an exploration which takes O(kn²) time steps and traverses O(kn) edges. Finally, the case where the underlying graph is a cycle is studied and tight linear bounds are provided on the number of edges traversed in the worst-case.
Cite as
Stefan Balev, Éric Sanlaville, and Antoine Toullalan. Brief Announcement: The Shortest Temporal Exploration Problem. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 18:1-18:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{balev_et_al:LIPIcs.SAND.2025.18,
author = {Balev, Stefan and Sanlaville, \'{E}ric and Toullalan, Antoine},
title = {{Brief Announcement: The Shortest Temporal Exploration Problem}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {18:1--18:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.18},
URN = {urn:nbn:de:0030-drops-230716},
doi = {10.4230/LIPIcs.SAND.2025.18},
annote = {Keywords: Graph Theory, Temporal Graph, Temporal Graph Exploration}
}
Document
Brief Announcement
Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols
Abstract
In the distributed localization problem (DLP), n anonymous robots (agents) A₀, …, A_{n-1} begin at arbitrary positions p₀, …, p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified coordinate system that accurately reflects the relative positions of all points, p₀, …, p_{n-1}, in S. Extensive research on DLP has primarily focused on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In this paper, however, we examine a minimalist, computationally efficient model of distributed computing in which agents have access to all pairwise distances, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v→_{ij} spanning points p_i and p_j (vector query model). We present here a leader-based localisation protocol with distance queries.
Cite as
Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 19:1-19:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gasieniec_et_al:LIPIcs.SAND.2025.19,
author = {G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
title = {{Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {19:1--19:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.19},
URN = {urn:nbn:de:0030-drops-230726},
doi = {10.4230/LIPIcs.SAND.2025.19},
annote = {Keywords: Population Protocols, Distributed Localisation}
}
Document
Brief Announcement
Brief Announcement: Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits
Abstract
In this paper, we study the problem of efficiently reducing geometric shapes into other such shapes in a distributed setting through size-changing operations. We develop distributed algorithms using the reconfigurable circuit model to enable fast node-to-node communication. Let n denote the number of nodes and k the number of turning points in the initial shape. We show that the system of nodes can reduce itself from any tree to a single node using only shrinking operations in O(k log n) rounds w.h.p. and any tree to its incompressible form in O(log n) rounds given prior knowledge of the incompressible nodes, or O(k log n) without it, w.h.p. We also give an algorithm to transform any tree to a topologically equivalent tree in O(k log n+log² n) rounds w.h.p. using both shrinking and growth operations. On the negative side, we show that one cannot hope for o(log² n)-round transformations for all shapes of Θ(log n) turning points.
Cite as
Nada Almalki, Siddharth Gupta, Othon Michail, and Andreas Padalkin. Brief Announcement: Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 20:1-20:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{almalki_et_al:LIPIcs.SAND.2025.20,
author = {Almalki, Nada and Gupta, Siddharth and Michail, Othon and Padalkin, Andreas},
title = {{Brief Announcement: Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {20:1--20:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.20},
URN = {urn:nbn:de:0030-drops-230730},
doi = {10.4230/LIPIcs.SAND.2025.20},
annote = {Keywords: growth process, shrinking process, collision avoidance, programmable matter}
}
Document
Brief Announcement
Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases
Abstract
We study the complexity of the directed periodic temporal graph realization problem. This work is motivated by the design of periodic schedules in public transport with constraints on the quality of service. Namely, we require that the fastest path between (important) pairs of vertices is upper bounded by a specified maximum duration, encoded in an upper distance matrix D. While previous work has considered the undirected version of the problem, the application in public transport schedule design requires the flexibility to assign different departure times to the two directions of an edge. A problem instance can only be feasible if all values of the distance matrix are at least shortest path distances. However, the task of realizing exact fastest path distances in a periodic temporal graph is often too restrictive. Therefore, we introduce a minimum slack parameter k that describes a lower bound on the maximum allowed waiting time on each path. We concentrate on tree topologies and provide a full characterization of the complexity landscape with respect to the period Δ and the minimum slack parameter k, showing a sharp threshold between NP-complete cases and cases which are always realizable. We also provide hardness results for the special case of period Δ = 2 for general directed and undirected graphs.
Cite as
Julia Meusel, Matthias Müller-Hannemann, and Klaus Reinhardt. Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 21:1-21:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{meusel_et_al:LIPIcs.SAND.2025.21,
author = {Meusel, Julia and M\"{u}ller-Hannemann, Matthias and Reinhardt, Klaus},
title = {{Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {21:1--21:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.21},
URN = {urn:nbn:de:0030-drops-230747},
doi = {10.4230/LIPIcs.SAND.2025.21},
annote = {Keywords: Temporal graph, fastest temporal path, graph realization, periodic scheduling}
}
Document
Brief Announcement
Brief Announcement: Exploring Word-Representable Temporal Graphs
Abstract
Word-representable graphs are a subset of graphs that may be represented by a word w over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices alternate in the word w. We generalise this notion to temporal graphs, constructing timesteps by partitioning the word into factors (contiguous subwords) such that no factor contains more than one copy of any given symbol. With this definition, we study the problem of exploration, asking for the fastest schedule such that a given agent may explore all n vertices of the graph. We show that if the corresponding temporal graph is connected in every timestep, we may explore the graph in 2δ n timesteps, where δ is the lowest degree of any vertex in the graph. In general, we show that, for any temporal graph represented by a word of length at least n(2dn + d), with a connected underlying graph, the full graph can be explored in 2 d n timesteps, where d is the diameter of the graph.
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Duncan Adamson. Brief Announcement: Exploring Word-Representable Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 22:1-22:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{adamson:LIPIcs.SAND.2025.22,
author = {Adamson, Duncan},
title = {{Brief Announcement: Exploring Word-Representable Temporal Graphs}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {22:1--22:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.22},
URN = {urn:nbn:de:0030-drops-230755},
doi = {10.4230/LIPIcs.SAND.2025.22},
annote = {Keywords: Temporal Graphs, Word-Representable Graphs}
}
Document
Brief Announcement
Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks
Abstract
For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Beyond what is contained in this brief announcement, we also investigate optimization variants of reachability, provide approximation results for maximizing species deletion, establish ETH-based lower bounds for NP-complete cases, and prove hardness for counting reaction sequences.
Cite as
Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie. Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 23:1-23:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{fu_et_al:LIPIcs.SAND.2025.23,
author = {Fu, Bin and Gomez, Timothy and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Rodriguez, Marco and Salinas, Adrian and Schweller, Robert and Wylie, Tim},
title = {{Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {23:1--23:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.23},
URN = {urn:nbn:de:0030-drops-230768},
doi = {10.4230/LIPIcs.SAND.2025.23},
annote = {Keywords: CRN, Chemical Reaction Network, Reachability, Void Reactions}
}
Document
Brief Announcement
Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly
Abstract
The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection.
The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in Γ, transferring the information to simulate Γ to each new tile. Supertiles may also asynchronously transition states according to the rules of Γ. This result also implies IU for pairwise asynchronous Cellular Automata.
Cite as
Tim Gomez, Elise Grizzell, Asher Haun, Ryan Knobel, Tom Peters, Robert Schweller, and Tim Wylie. Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 24:1-24:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gomez_et_al:LIPIcs.SAND.2025.24,
author = {Gomez, Tim and Grizzell, Elise and Haun, Asher and Knobel, Ryan and Peters, Tom and Schweller, Robert and Wylie, Tim},
title = {{Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly}},
booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
pages = {24:1--24:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-368-3},
ISSN = {1868-8969},
year = {2025},
volume = {330},
editor = {Meeks, Kitty and Scheideler, Christian},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.24},
URN = {urn:nbn:de:0030-drops-230772},
doi = {10.4230/LIPIcs.SAND.2025.24},
annote = {Keywords: Intrinsic Universality, Tile Automata, Cellular Automata, Self-assembly}
}