arXiv subjects

Jessica Enright

Publications and source records attributed to Jessica Enright.

At least 19 recordsLinked to original sources

arXiv2026

Temporal Role Colouring

A role colouring of a graph $G$ is an assignment of colours to the vertices of $G$ such that two vertices of the same colour have identical sets of colours in their neighbourhoods. This model is used to capture the idea of vertices having roles in a contact network, consistent with the set of roles of their contacts. We define an extension of the role colouring problem to temporal graphs. Temporal roles are defined via an automaton with states and transitions capturing both the current colour of a vertex and information about its current and past adjacencies. We show, by a reduction from the static problem, that the temporal role colouring problem is NP-complete. To contend with this intractability, we explore several parameterisations. We give fixed-parameter tractability results with respect to the number of states of the automaton combined with either the vertex-interval-membership width or the tree-interval-membership width of the temporal graph. We further show the problem is in FPT parameterised by the treewidth of the underlying graph, the lifetime of the temporal graph and the number of colours combined.

cs.DM↗

arXiv2026

$O(n +f(k))$: Truly Linear FPT

Parameterized complexity has always been concerned with practical computing: by confining combinatorial explosion to a secondary parameter $k$, one can uncover why and how many NP-hard problems are effectively tackled in practice. Today, however, the scale of data has changed: scientists study Big Data, which is so large that even quadratic dependence in the total input size $n$ is unaffordable. Therefore, what constitutes a practical algorithm has also changed. Classically, parameterized complexity is blind to the difference between defining fixed parameter tractability multiplicatively (i.e. $f(k) \cdot n^c$) or additively (i.e. $f(k) + n^c$). But what if the constant $c$ is one and we require true linearity, is this distinction still inconsequential? Here, we define and explore Truly Linear FPT (TLFPT) -- that is $O(n)+f(k)$ -- and show that it is a strict subset of Linear FPT (LFPT) -- that is $O(n) \cdot f(k)$ -- via diagonalization. Populating TLFPT requires careful consideration of linear-time algorithmics and data structures. We meet many inhabitants of TLFPT: SAT, Vertex Cover, Min-Max Matching, $(n-k)$-Coloring, Diverse Pair of Matchings, $k$-Path, and $H$-Coloring. Our parameterizations are equally varied. Beyond classical parameters like solution size, we leverage two parameters, treedepth and BFS-width, which are particularly well-suited to the TLFPT regime. We do so by developing techniques based on depth- and breadth-first search. For parameterized complexity to be of service to the scientific community, we need to contend with Big Data. For sufficiently large inputs, FPT beyond linear may not suffice. Thus, there is a practical and theoretical need for more ambitious goals. TLFPT is a first step forward.

cs.CC↗

arXiv2026

FO and MSO Model Checking on Temporal Graphs

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 (VIM) width and tree-interval-membership (TIM) width, parameters which 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 degree to the parameters VIM and TIM width, 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.

cs.DM↗

arXiv2025

Approximating temporal modularity on graphs of small underlying treewidth

Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete timesteps; such graphs offer a more realistic model of many real-world networks in which connections between entities (for example, between individuals in a social network) evolve over time. Computing modularity is notoriously difficult: it is NP-hard even to approximate in general, and only admits efficient exact algorithms in very restricted special cases. Our main result is that a multiplicative approximation to temporal modularity can be computed efficiently when the underlying graph has small treewidth. This generalises a similar approximation algorithm for the static case, but requires some substantially new ideas to overcome technical challenges associated with the temporal nature of the problem.

math.CO↗

arXiv2025

Temporal Orienteering with Changing Fuel Costs

The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one endpoint and the time we arrive at the other endpoint. This mirrors applications such as travel between orbiting objects where fuel costs are dependent on both the departure time and the length of time spent travelling. In defining this problem, we introduce a natural generalisation of the standard notion of temporal graphs: the pair consisting of the graph of the sites and a cost function, in which costs as well as shortest travel times between pairs of objects change over time. We believe this model is likely to be of independent interest. The problem of deciding whether a stated goal is feasible is easily seen to be NP-complete; we investigate three different ways to restrict the input which lead to efficient algorithms. These include the number of times an edge can be used, an analogue of vertex-interval-membership width, and the number of sites to be visited.

cs.DM↗

arXiv2025

Improving wastewater-based epidemiology through strategic placement of samplers

Wastewater-based epidemiology (WBE) is a fast emerging method for passively monitoring diseases in a population. By measuring the concentrations of pathogenic materials in wastewater, WBE negates demographic biases in clinical testing and healthcare demand, and may act as a leading indicator of disease incidence. For a WBE system to be effective, it should detect the presence of a new pathogen of concern early enough and with enough precision that it can still be localised and contained. In this study, then, we show how multiple wastewater sensors can be strategically placed across a wastewater system, to detect the presence of disease faster than if sampling was done at the wastewater treatment plant only. Our approach generalises to any tree-like network and takes into account the structure of the network and how the population is distributed over it. We show how placing sensors further upstream from the treatment plant improves detection sensitivity and can inform how an outbreak is evolving in different geographical regions. However, this improvement diminishes once individual-level shedding is modelled as highly dispersed. With overdispersed shedding, we show using real COVID-19 cases in Scotland that broad trends in disease incidence (i.e., whether the epidemic is in growth or decline) can still be reasonably estimated from the wastewater signal once incidence exceeds about 5 infections per day.

q-bio.PE↗

arXiv2025

Families of tractable problems with respect to vertex-interval-membership width and its generalisations

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.

cs.DM↗

arXiv2025

Parameterised algorithms for temporally satisfying reconfiguration problems

Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the vertex-selection problem at each time such that we can reconfigure from one solution to the next. We can think of each solution in the sequence as a set of vertices with tokens placed on them; our reconfiguration model allows us to slide tokens along active edges of a temporal graph at each time-step. We show that it is possible to efficiently check whether one solution can be reconfigured to another, and show that approximation results on the static vertex-selection problem can be adapted with a lifetime factor to the reconfiguration version. Our main contributions are fixed-parameter tractable algorithms with respect to: enumeration time of the related static problem; the combination of temporal neighbourhood diversity and lifetime of the input temporal graph; and the combination of lifetime and treewidth of the footprint graph.

cs.DS↗

arXiv2024

Temporal Triadic Closure: Finding Dense Structures in Social Networks That Evolve

A graph G is c-closed if every two vertices with at least c common neighbors are adjacent to each other. Introduced by Fox, Roughgarden, Seshadhri, Wei and Wein [ICALP 2018, SICOMP 2020], this definition is an abstraction of the triadic closure property exhibited by many real-world social networks, namely, friends of friends tend to be friends themselves. Social networks, however, are often temporal rather than static -- the connections change over a period of time. And hence temporal graphs, rather than static graphs, are often better suited to model social networks. Motivated by this, we introduce a definition of temporal c-closed graphs, in which if two vertices u and v have at least c common neighbors during a short interval of time, then u and v are adjacent to each other around that time. Our pilot experiments show that several real-world temporal networks are c-closed for rather small values of c. We also study the computational problems of enumerating maximal cliques and similar dense subgraphs in temporal c-closed graphs; a clique in a temporal graph is a subgraph that lasts for a certain period of time, during which every possible edge in the subgraph becomes active often enough, and other dense subgraphs are defined similarly. We bound the number of such maximal dense subgraphs in a temporal c-closed graph that evolves slowly, and thus show that the corresponding enumeration problems admit efficient algorithms; by slow evolution, we mean that between consecutive time-steps, the local change in adjacencies remains small. Our work also adds to a growing body of literature on defining suitable structural parameters for temporal graphs that can be leveraged to design efficient algorithms.

cs.DS↗

arXiv2024

Reachability in temporal graphs under perturbation

Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely to perfectly reflect reality, especially with respect to the precise times at which edges appear. To reflect this uncertainty, we consider a model in which some number $\zeta$ of edge appearances may have their timestamps perturbed by $\pm\delta$ for some $\delta$. Within this model, we investigate temporal reachability and consider the problem of determining the maximum number of vertices any vertex can reach under these perturbations. We show that this problem is intractable in general but is efficiently solvable when $\zeta$ is sufficiently large. We also give algorithms which solve this problem in several restricted settings. We complement this with some contrasting results concerning the complexity of related temporal eccentricity problems under perturbation.

cs.DM↗

arXiv2024

Structural Parameters for Dense Temporal Graphs

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.

cs.DM↗

arXiv2023

Cops and Robbers on Multi-Layer Graphs

We generalise the popular cops and robbers game to multi-layer graphs, where each cop and the robber are restricted to a single layer (or set of edges). We show that initial intuition about the best way to allocate cops to layers is not always correct, and prove that the multi-layer cop number is neither bounded from above nor below by any increasing function of the cop numbers of the individual layers. We determine that it is NP-hard to decide if $k$ cops are sufficient to catch the robber, even if every cop layer is a tree and a set of isolated vertices. However, we give a polynomial time algorithm to determine if $k$ cops can win when the robber layer is a tree. Additionally, we investigate a question of worst-case divisions of a simple graph into layers: given a simple graph $G$, what is the maximum number of cops required to catch a robber over all multi-layer graphs where each edge of $G$ is in at least one layer and all layers are connected? For cliques, suitably dense random graphs, and graphs of bounded treewidth, we determine this parameter up to multiplicative constants. Lastly we consider a multi-layer variant of Meyniel's conjecture, and show the existence of an infinite family of graphs whose multi-layer cop number is bounded from below by a constant times $n / \log n$, where $n$ is the number of vertices in the graph.

math.CO↗

arXiv2022

Bovine Tuberculosis in Britain: identifying signatures of polarisation and controversy on Twitter

Approaches to disease control are influenced by and reflected in public opinion, and the two are intrinsically entwined. Bovine tuberculosis (bTB) in British cattle and badgers is one example where there is a high degree of polarisation in opinion. Bovine viral diarrhoea (BVD), on the other hand, does not have the same controversy. In this paper we examine how language subjectivity on Twitter differs when comparing the discourses surrounding bTB and BVD, using a combination of network analysis and language and sentiment analysis. That data used for this study was collected from the Twitter public API over a two-year period. We investigated the network structure, language content, and user profiles of tweets featuring both diseases. While analysing network structure showed little difference between the two disease topics, elements of the structure allowed us to better investigate the language structure and profile of users. We found distinct differences between the language and sentiment used in tweets about each disease, and in the profile of the users who were doing the tweeting. We hope that this will guide further investigation and potential avenues for surveillance or the control of misinformation.

cs.SI↗

arXiv2022

Visualization for Epidemiological Modelling: Challenges, Solutions, Reflections & Recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs -- a series of ideas, approaches and methods taken from existing visualization research and practice -- deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type; and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/

cs.HC↗

arXiv2022

Making Life More Confusing for Firefighters

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 civilians 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.

cs.DS↗

arXiv2022

Counting Temporal Paths

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 prameterised 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 proved several exact and approximate FPT-algorithms for special cases.

cs.DS↗

arXiv2021

Recognising the overlap graphs of subtrees of restricted trees is hard

The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs in open. The complexities of recognising many subclasses of SOGs are known. We consider several subclasses of SOGs by restricting the underlying tree. For a fixed integer $k \geq 3$, we consider: \begin{my_itemize} \item The overlap graphs of subtrees in a tree where that tree has $k$ leaves \item The overlap graphs of subtrees in trees that can be derived from a given input tree by subdivision and have at least 3 leaves \item The overlap and intersection graphs of paths in a tree where that tree has maximum degree $k$ \end{my_itemize} We show that the recognition problems of these classes are NP-complete. For all other parameters we get circle graphs, well known to be polynomially recognizable.

cs.CC↗

arXiv2021

FAIR Data Pipeline: provenance-driven data management for traceable scientific workflows

Modern epidemiological analyses to understand and combat the spread of disease depend critically on access to, and use of, data. Rapidly evolving data, such as data streams changing during a disease outbreak, are particularly challenging. Data management is further complicated by data being imprecisely identified when used. Public trust in policy decisions resulting from such analyses is easily damaged and is often low, with cynicism arising where claims of "following the science" are made without accompanying evidence. Tracing the provenance of such decisions back through open software to primary data would clarify this evidence, enhancing the transparency of the decision-making process. Here, we demonstrate a Findable, Accessible, Interoperable and Reusable (FAIR) data pipeline developed during the COVID-19 pandemic that allows easy annotation of data as they are consumed by analyses, while tracing the provenance of scientific outputs back through the analytical source code to data sources. Such a tool provides a mechanism for the public, and fellow scientists, to better assess the trust that should be placed in scientific evidence, while allowing scientists to support policy-makers in openly justifying their decisions. We believe that tools such as this should be promoted for use across all areas of policy-facing research.

q-bio.QM↗