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Documents authored by Schoeters, Jason

Document
DOI: 10.4230/LIPIcs.SAND.2025.8
Matching and Edge Cover in Temporal Graphs

Authors: Lapo Cioni, Riccardo Dondi, Andrea Marino, Jason Schoeters, and Ana Silva

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

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
DOI: 10.4230/LIPIcs.SAND.2025.9
Spanner Enumeration for Temporal Graphs

Authors: Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

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
DOI: 10.4230/LIPIcs.SAND.2024.8
On Inefficiently Connecting Temporal Networks

Authors: Esteban Christiann, Eric Sanlaville, and Jason Schoeters

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

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
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.134
Temporal Cliques Admit Sparse Spanners

Authors: Arnaud Casteigts, Joseph G. Peters, and Jason Schoeters

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Let G=(V,E) be an undirected graph on n vertices and lambda:E -> 2^{N} a mapping that assigns to every edge a non-empty set of positive integer labels. These labels can be seen as discrete times when the edge is present. Such a labeled graph {G}=(G,lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex. In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse subset of edges can always be found whose labels suffice to preserve temporal connectivity - a temporal spanner. Axiotis and Fotakis (ICALP 2016) answered negatively by exhibiting a family of Theta(n^2)-dense temporal graphs which admit no temporal spanner of density o(n^2). The natural question is then whether sparse temporal spanners always exist in some classes of dense graphs. In this paper, we answer this question affirmatively, by showing that if the underlying graph G is a complete graph, then one can always find temporal spanners of density O(n log n). The best known result for complete graphs so far was that spanners of density binom{n}{2}- floor[n/4] = O(n^2) always exist. Our result is the first positive answer as to the existence of o(n^2) sparse spanners in adversarial instances of temporal graphs since the original question by Kempe et al., focusing here on complete graphs. The proofs are constructive and directly adaptable as an algorithm.
Cite as

Arnaud Casteigts, Joseph G. Peters, and Jason Schoeters. Temporal Cliques Admit Sparse Spanners. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 134:1-134:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{casteigts_et_al:LIPIcs.ICALP.2019.134,
  author =	{Casteigts, Arnaud and Peters, Joseph G. and Schoeters, Jason},
  title =	{{Temporal Cliques Admit Sparse Spanners}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{134:1--134:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.134},
  URN =		{urn:nbn:de:0030-drops-107108},
  doi =		{10.4230/LIPIcs.ICALP.2019.134},
  annote =	{Keywords: Dynamic networks, Temporal graphs, Temporal connectivity, Sparse spanners}
}
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