Document

**Published in:** LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Temporal graphs provide a useful model for many real-world networks. Unfortunately, the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which describe tractable cases by simultaneously restricting the underlying structure and the times at which edges appear in the graph. These all rely on the temporal graph being sparse in some sense. We introduce temporal analogues of three increasingly restrictive static graph parameters - cliquewidth, modular-width and neighbourhood diversity - which take small values for highly structured temporal graphs, even if a large number of edges are active at each timestep. The computational problems solvable efficiently when the temporal cliquewidth of the input graph is bounded form a subset of those solvable efficiently when the temporal modular-width is bounded, which is in turn a subset of problems efficiently solvable when the temporal neighbourhood diversity is bounded. By considering specific temporal graph problems, we demonstrate that (up to standard complexity theoretic assumptions) these inclusions are strict.

Jessica Enright, Samuel D. Hand, Laura Larios-Jones, and Kitty Meeks. Structural Parameters for Dense Temporal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{enright_et_al:LIPIcs.MFCS.2024.52, author = {Enright, Jessica and Hand, Samuel D. and Larios-Jones, Laura and Meeks, Kitty}, title = {{Structural Parameters for Dense Temporal Graphs}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {52:1--52:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.52}, URN = {urn:nbn:de:0030-drops-206082}, doi = {10.4230/LIPIcs.MFCS.2024.52}, annote = {Keywords: Graph algorithms, Parameterized Algorithms, Temporal Graphs} }

Document

**Published in:** LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

The betweenness centrality of a vertex v is an important centrality measure that quantifies how many optimal paths between pairs of other vertices visit v. Computing betweenness centrality in a temporal graph, in which the edge set may change over discrete timesteps, requires us to count temporal paths that are optimal with respect to some criterion. For several natural notions of optimality, including foremost or fastest temporal paths, this counting problem reduces to #TEMPORAL PATH, the problem of counting all temporal paths between a fixed pair of vertices; like the problems of counting foremost and fastest temporal paths, #TEMPORAL PATH is #P-hard in general. Motivated by the many applications of this intractable problem, we initiate a systematic study of the parameterised and approximation complexity of #TEMPORAL PATH. We show that the problem presumably does not admit an FPT-algorithm for the feedback vertex number of the static underlying graph, and that it is hard to approximate in general. On the positive side, we prove several exact and approximate FPT-algorithms for special cases.

Jessica Enright, Kitty Meeks, and Hendrik Molter. Counting Temporal Paths. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{enright_et_al:LIPIcs.STACS.2023.30, author = {Enright, Jessica and Meeks, Kitty and Molter, Hendrik}, title = {{Counting Temporal Paths}}, booktitle = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)}, pages = {30:1--30:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-266-2}, ISSN = {1868-8969}, year = {2023}, volume = {254}, editor = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.30}, URN = {urn:nbn:de:0030-drops-176829}, doi = {10.4230/LIPIcs.STACS.2023.30}, annote = {Keywords: Temporal Paths, Temporal Graphs, Parameterised Counting, Approximate Counting, #P-hard Counting Problems, Temporal Betweenness Centrality} }

Document

**Published in:** LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

It is well known that fighting a fire is a hard task. The Firefighter problem asks how to optimally deploy firefighters to defend the vertices of a graph from a fire. This problem is NP-Complete on all but a few classes of graphs. Thankfully, firefighters do not have to work alone, and are often aided by the efforts of good natured civillians who slow the spread of a fire by maintaining firebreaks when they are able. We will show that this help, although well-intentioned, unfortunately makes the optimal deployment of firefighters an even harder problem. To model this scenario we introduce the Temporal Firefighter problem, an extension of Firefighter to temporal graphs. We show that Temporal Firefighter is also NP-Complete, and remains so on all but one of the underlying classes of graphs on which Firefighter is known to have polynomial time solutions. This motivates us to explore making use of the temporal structure of the graph in our search for tractability, and we conclude by presenting an FPT algorithm for Temporal Firefighter with respect to the temporal graph parameter vertex-interval-membership-width.

Samuel D. Hand, Jessica Enright, and Kitty Meeks. Making Life More Confusing for Firefighters. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{hand_et_al:LIPIcs.FUN.2022.15, author = {Hand, Samuel D. and Enright, Jessica and Meeks, Kitty}, title = {{Making Life More Confusing for Firefighters}}, booktitle = {11th International Conference on Fun with Algorithms (FUN 2022)}, pages = {15:1--15:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-232-7}, ISSN = {1868-8969}, year = {2022}, volume = {226}, editor = {Fraigniaud, Pierre and Uno, Yushi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.15}, URN = {urn:nbn:de:0030-drops-159851}, doi = {10.4230/LIPIcs.FUN.2022.15}, annote = {Keywords: Temporal graphs, Spreading processes, Parameterised complexity} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

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

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

Copy BibTex To Clipboard

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

Document

**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information or behaviour spread over social networks, biological diseases spreading over contact or trade networks, and the potential flow of goods over logistical infrastructure. Often, the networks over which these processes spread are dynamic in nature, and can be modeled with graphs whose structure is subject to discrete changes over time, i.e. with temporal graphs. Here, we consider temporal graphs in which edges are available at specified timesteps, and study the problem of deleting edges from a given temporal graph in order to reduce the number of vertices (temporally) reachable from a given starting point. This could be used to control the spread of a disease, rumour, etc. in a temporal graph. In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices using a temporally-feasible path (i.e. a path, along which the times of the edge availabilities increase). We introduce a natural deletion problem for temporal graphs and we provide positive and negative results on its computational complexity, both in the traditional and the parameterised sense (subject to various natural parameters), as well as addressing the approximability of this problem.

Jessica Enright, Kitty Meeks, George B. Mertzios, and Viktor Zamaraev. Deleting Edges to Restrict the Size of an Epidemic in Temporal Networks. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{enright_et_al:LIPIcs.MFCS.2019.57, author = {Enright, Jessica and Meeks, Kitty and Mertzios, George B. and Zamaraev, Viktor}, title = {{Deleting Edges to Restrict the Size of an Epidemic in Temporal Networks}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {57:1--57:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.57}, URN = {urn:nbn:de:0030-drops-110010}, doi = {10.4230/LIPIcs.MFCS.2019.57}, annote = {Keywords: Temporal networks, spreading processes, graph modification, parameterised complexity} }

Document

**Published in:** LIPIcs, Volume 49, 8th International Conference on Fun with Algorithms (FUN 2016)

Mouse Maze is a Flash game about Squeaky, a mouse who has to navigate a subset of the grid using a simple deterministic rule, which naturally generalises to a game on arbitrary graphs with some interesting chaotic dynamics. We present the results of some evolutionary algorithms which generate graphs which effectively trap Squeaky in the maze for long periods of time, and some theoretical results on how long he can be trapped. We then discuss what would happen to Squeaky if he couldn't count, and present some open problems in the area.

Jessica Enright and John D. Faben. Building a Better Mouse Maze. In 8th International Conference on Fun with Algorithms (FUN 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 49, pp. 15:1-15:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{enright_et_al:LIPIcs.FUN.2016.15, author = {Enright, Jessica and Faben, John D.}, title = {{Building a Better Mouse Maze}}, booktitle = {8th International Conference on Fun with Algorithms (FUN 2016)}, pages = {15:1--15:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-005-7}, ISSN = {1868-8969}, year = {2016}, volume = {49}, editor = {Demaine, Erik D. and Grandoni, Fabrizio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2016.15}, URN = {urn:nbn:de:0030-drops-58743}, doi = {10.4230/LIPIcs.FUN.2016.15}, annote = {Keywords: graph, evolutionary, genetic algorithm, traversal} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail