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In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted…

Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…

Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our…

Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original…

We propose a protocol that, given a communication network, computes a subnetwork such that, for every pair $(u,v)$ of nodes connected in the original network, there is a minimum-energy path between $u$ and $v$ in the subnetwork (where a…

The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature…

We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsically ill-posed, exhibiting…

This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Systems of networked mobile robots, such as unmanned aerial or ground vehicles, will play important roles in future military and commercial applications. The communications for such systems will typically be over wireless links and may…

We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure…

The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…

We focus on robust, survivable communication networks, where network links and nodes are affected by an uncertainty set. In this sense, any network links might fail. Besides, a signal can only travel a maximum distance before its quality…

We propose network coding as an energy efficient data transmission technique in core networks with non-bypass and bypass routing approaches. The improvement in energy efficiency is achieved through reduction in the traffic flows passing…

This research studies a non-convex geometric optimization problem arising from the field of optical wireless power transfer. In the considered optimization problem, the cost function is a sum of negatively and fractionally powered distances…

Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces,…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…

The maximum achievable capacity from source to destination in a network is limited by the min-cut max-flow bound; this serves as a converse limit. In practice, link capacities often fluctuate due to dynamic network conditions. In this work,…

We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…