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Documents authored by Enright, Jessica

Document
DOI: 10.4230/LIPIcs.SAND.2026.4
Families of Tractable Problems with Respect to Vertex-Interval-Membership Width and Its Generalisations

Authors: Jessica Enright, Samuel D. Hand, Laura Larios-Jones, and Kitty Meeks

Published in: LIPIcs, Volume 373, 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)

Abstract
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than their static counterparts. To contend with this, there has been recent work devising parameters for which temporal problems become tractable. One such parameter is vertex-interval-membership (VIM) width. Broadly, this gives a bound on the number of vertices we need to keep track of at any given time to solve many problems. Our contributions are two-fold. Firstly, we introduce a new parameter, tree-interval-membership (TIM) width, that generalises both VIM width and several existing generalisations. Secondly, we provide meta-algorithms for both VIM and TIM width which can be used to prove fixed-parameter-tractability for large families of problems, bypassing the need to give involved dynamic programming arguments for every problem. In doing this, we provide a characterisation of problems in FPT with respect to both parameters. We apply these algorithms to temporal versions of Hamiltonian path, dominating set, matching, and edge deletion to limit maximum reachability.
Cite as

Jessica Enright, Samuel D. Hand, Laura Larios-Jones, and Kitty Meeks. Families of Tractable Problems with Respect to Vertex-Interval-Membership Width and Its Generalisations. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{enright_et_al:LIPIcs.SAND.2026.4,
  author =	{Enright, Jessica and Hand, Samuel D. and Larios-Jones, Laura and Meeks, Kitty},
  title =	{{Families of Tractable Problems with Respect to Vertex-Interval-Membership Width and Its Generalisations}},
  booktitle =	{5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)},
  pages =	{4:1--4:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-427-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{373},
  editor =	{Mertzios, George B. and Richa, Andr\'{e}a W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.4},
  URN =		{urn:nbn:de:0030-drops-262386},
  doi =		{10.4230/LIPIcs.SAND.2026.4},
  annote =	{Keywords: Graph algorithms, Parameterized Algorithms, Temporal Graphs}
}
Document
DOI: 10.4230/LIPIcs.SAND.2026.9
FO and MSO Model Checking on Temporal Graphs

Authors: Michelle Döring, Jessica Enright, Laura Larios-Jones, and George Skretas

Published in: LIPIcs, Volume 373, 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)

Abstract
Algorithmic meta-theorems provide an important tool for showing tractability of graph problems on graph classes defined by structural restrictions. While such results are well established for static graphs, corresponding frameworks for temporal graphs are comparatively limited. In this work, we revisit past applications of logical meta-theorems to temporal graphs and develop an extended unifying logical framework. Our first contribution is the introduction of logical encodings for the parameters vertex-interval-membership width (vim) and tree-interval-membership width (tim), parameters that capture the signature of vertex and component activity over time. Building on this, we extend existing monadic second-order (MSO) meta-theorems for bounded lifetime and temporal total degree to the parameters vim and tim, and establish novel first-order (FO) meta-theorems for all four parameters. Finally, we signpost a modular lexicon of reusable FO and MSO formulas for a broad range of temporal graph problems, and give an example. This lexicon allows new problems to be expressed compositionally and directly yields fixed-parameter tractability results across the four parameters we consider.
Cite as

Michelle Döring, Jessica Enright, Laura Larios-Jones, and George Skretas. FO and MSO Model Checking on Temporal Graphs. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{doring_et_al:LIPIcs.SAND.2026.9,
  author =	{D\"{o}ring, Michelle and Enright, Jessica and Larios-Jones, Laura and Skretas, George},
  title =	{{FO and MSO Model Checking on Temporal Graphs}},
  booktitle =	{5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-427-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{373},
  editor =	{Mertzios, George B. and Richa, Andr\'{e}a W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.9},
  URN =		{urn:nbn:de:0030-drops-262430},
  doi =		{10.4230/LIPIcs.SAND.2026.9},
  annote =	{Keywords: temporal graphs, dynamic graphs, time-varying graphs, parameterized complexity, logic, meta-theorems, monadic second-order logic, first-order logic, treewidth, planar, nowhere dense, lifetime, temporal total degree, vertex-interval membership width, tree-interval membership width}
}
Document
DOI: 10.4230/LIPIcs.SAND.2026.14
Robust Temporal Cut

Authors: Jessica Enright, Thomas Erlebach, Kitty Meeks, and Nils Morawietz

Published in: LIPIcs, Volume 373, 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)

Abstract
In this paper we introduce the Robust Temporal Cut problem (RTC) defined as follows: For a given temporal graph with designated source node s and destination node z, and parameters δ and k, remove a minimum number of time edges so that, even if an adversary can adjust the time labels of up to k of the remaining time edges by adding or subtracting values bounded by δ, no temporal s-z path exists. We study the classical and parameterized complexity of RTC. In particular, we show for both strict and non-strict temporal paths that RTC is NP-complete for any combination of k ≥ 1 and δ ≥ 1 and W[1]-hard for parameter solution size or vertex interval membership width plus pathwidth of the underlying graph. Furthermore, we give approximation algorithms and FPT algorithms for parameters including temporal neighborhood diversity plus solution size, timed vertex cover size, and vertex cover size of the underlying graph plus solution size.
Cite as

Jessica Enright, Thomas Erlebach, Kitty Meeks, and Nils Morawietz. Robust Temporal Cut. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{enright_et_al:LIPIcs.SAND.2026.14,
  author =	{Enright, Jessica and Erlebach, Thomas and Meeks, Kitty and Morawietz, Nils},
  title =	{{Robust Temporal Cut}},
  booktitle =	{5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-427-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{373},
  editor =	{Mertzios, George B. and Richa, Andr\'{e}a W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.14},
  URN =		{urn:nbn:de:0030-drops-262480},
  doi =		{10.4230/LIPIcs.SAND.2026.14},
  annote =	{Keywords: temporal graphs, minimum cut, parameterized complexity, FPT algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.52
Structural Parameters for Dense Temporal Graphs

Authors: Jessica Enright, Samuel D. Hand, Laura Larios-Jones, and Kitty Meeks

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

Abstract
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.
Cite as

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)

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@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
DOI: 10.4230/LIPIcs.STACS.2023.30
Counting Temporal Paths

Authors: Jessica Enright, Kitty Meeks, and Hendrik Molter

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

Abstract
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.
Cite as

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)

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@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
DOI: 10.4230/LIPIcs.FUN.2022.15
Making Life More Confusing for Firefighters

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

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

Abstract
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.
Cite as

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)

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@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
DOI: 10.4230/LIPIcs.SAND.2022.22
Brief Announcement: The Temporal Firefighter Problem

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

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

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

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

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@InProceedings{hand_et_al:LIPIcs.SAND.2022.22,
  author =	{Hand, Samuel D. and Enright, Jessica and Meeks, Kitty},
  title =	{{Brief Announcement: The Temporal Firefighter Problem}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{22:1--22:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.22},
  URN =		{urn:nbn:de:0030-drops-159644},
  doi =		{10.4230/LIPIcs.SAND.2022.22},
  annote =	{Keywords: Temporal graphs, Spreading processes, Parameterised complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.57
Deleting Edges to Restrict the Size of an Epidemic in Temporal Networks

Authors: Jessica Enright, Kitty Meeks, George B. Mertzios, and Viktor Zamaraev

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

Abstract
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.
Cite as

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)

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@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
DOI: 10.4230/LIPIcs.FUN.2016.15
Building a Better Mouse Maze

Authors: Jessica Enright and John D. Faben

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

Abstract
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.
Cite as

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)

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@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}
}
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