Jessica Enright’s research while affiliated with University of Glasgow and other places

A graph G is c-closed if every two vertices with at least c common neighbors are adjacent to each other. 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 other 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; 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.

This work investigates the parameterised complexity of counting temporal paths. The problem of counting temporal paths is mainly motivated by temporal betweenness computation. 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.

Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporal 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. 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 graph; and the combination of lifetime and treewidth of the footprint graph.

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.

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter.

In East Africa, climate change is likely to profoundly impact livestock management and the potential spread of infectious diseases. Here, we developed a network model to describe livestock movements to grazing and watering sites, fitted it to data from the Serengeti district of Tanzania, and used it to explore how projected changes in resource availability due to climate change could impact future network structures and therefore infectious disease risks, using 2050 and 2080 as exemplar scenarios. Our modelled networks show increased connections between villages in grazing and watering networks, with connectivity increasing further in the future in correspondence with changes in vegetation and water availability. Our analyses show that targeted interventions to efficiently control regional disease spread may become more difficult, as village connectivity increases and disease vulnerability becomes more evenly distributed. This analysis also provides proof of principle for a novel approach applicable to agropastoral settings across many developing countries, where livestock trade plays a crucial role in maintaining local livelihoods but also in spreading disease.

Salmonid aquaculture is an important source of nutritious food with more than 2 million tonnes of fish produced each year (Food and Agriculture Organisation of the United Nations, 2019). In most salmon producing countries, sea lice represent a major barrier to the sustainability of salmonid aquaculture. This issue is exacerbated by widespread resistance to chemical treatments on both sides of the Atlantic. Regulation for sea lice management mostly involves reporting lice counts and treatment thresholds, which depending on interpretation may encourage preemptive treatments. We have developed a stochastic simulation model of sea lice infestation including the lice life-cycle, genetic resistance to treatment, a wildlife reservoir, salmon growth and stocking practices in the context of infestation, and coordination of treatment between farms. Farms report infestation levels to a central organisation, and may then cooperate or not when coordinated treatment is triggered. Treatment practice then impacts the level of resistance in the surrounding sea lice population. Our simulation finds that treatment drives selection for resistance and coordination between managers is key. We also find that position in the hydrologically-derived network of farms can impact individual farm infestation levels and the topology of this network can impact overall infestation and resistance. We show how coordination and triggering of treatment alongside varying hydrological topology of farm connections affects the evolution of lice resistance, and thus optimise salmon quality within socio-economic and environmental constraints. Network topology drives infestation levels in cages, treatments, and hence treatment-driven resistance. Thus farmer behaviour may be highly dependent on hydrologically position and local level of infestation.