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We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…

We study the NP-hard Fair Connected Districting problem recently proposed by Stoica et al. [AAMAS 2020]: Partition a vertex-colored graph into k connected components (subsequently referred to as districts) so that in every district the most…

We consider protection problems in multilayer networks. In single-layer networks, a pair of disjoint paths can be used to provide protection for a source-destination pair. However, this approach cannot be directly applied to layered…

Conveying environmental data has grown interest in encouraging the adoption of eco-friendly lifestyles through data-driven strategies. This scope appeals to data visualizations representing the environmental purpose. For example, previous…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Camera traps have long been used by wildlife researchers to monitor and study animal behavior, population dynamics, habitat use, and species diversity in a non-invasive and efficient manner. While data collection from the field has…

An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. When k = 1 the complexity of the problem is polynomial. In this paper, we further find the…

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…

In the network activation problem, each edge in a graph is associated with an activation function, that decides whether the edge is activated from node-weights assigned to its end-nodes. The feasible solutions of the problem are the…

Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…

Recently, the selection-recombination equation with a single selected site and an arbitrary number of neutral sites was solved by means of the ancestral selection-recombination graph. Here, we introduce a more accessible approach, namely…

Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…

In an effort to effectively model observed patterns in the spatial configuration of individuals of multiple species in nature, we introduce the saturated pairwise interaction Gibbs point process. Its main strength lies in its ability to…

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

A recent problem in community ecology lies in defining structures behind matrices of species interactions. The interest in this area is to quantify the nestedness degree of the matrix after its maximal packing. In this work we evaluate…

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…

Understanding the architectural subtleties of ecological networks, believed to confer them enhanced stability and robustness, is a subject of outmost relevance. Mutualistic interactions have been profusely studied and their corresponding…

Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…