Related papers: AC-Feasibility on Tree Networks is NP-Hard
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
In this work, we answer an open problem in the study of phylogenetic networks. Phylogenetic trees are rooted binary trees in which all edges are directed away from the root, whereas phylogenetic networks are rooted acyclic digraphs. For the…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
Bottleneck Steiner networks model energy consumption in wireless ad-hoc networks. The task is to design a network spanning a given set of terminals and at most $k$ Steiner points such that the length of the longest edge is minimised. The…
We employ simulations of model proteins to study folding on rugged energy landscapes. We construct ``first-passage'' networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to…
Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…
High wind energy penetration critically challenges the economic dispatch of current and future power systems. Supply and demand must be balanced at every bus of the grid, while respecting transmission line ratings and accounting for the…
Consideration of generation, load and network uncertainties in modern transmission network expansion planning (TNEP) is gaining interest due to large-scale integration of renewable energy sources with the existing grid. However, it is a…
We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We…
Solving for globally optimal line switching decisions in AC transmission grids can be intractability slow. Machine learning (ML) models, meanwhile, can be trained to predict near-optimal decisions at a fraction of the speed. Verifying the…
Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a…
We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable…
The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem.…
We address the problem of maintaining high voltage power transmission networks in security at all time. This requires that power flowing through all lines remain below a certain nominal thermal limit above which lines might melt, break or…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
With the integration of Renewable Energy Sources (RESs), the power network must be robust to handle the system's uncertain scenarios. DC Transmission Expansion Planning (TEP) plans are generally not feasible for the AC network. A first…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…