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The AC optimal power flow (AC-OPF) problem is essential for power system operations, but its non-convex nature makes it challenging to solve. A widely used simplification is the linearized DC optimal power flow (DC-OPF) problem, which can…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
We study the complexity of the Virtual Network Embedding Problem (VNE), which is the combinatorial core of several telecommunication problems related to the implementation of virtualization technologies, such as Network Slicing. VNE is to…
Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e.\ networks with more degrees of freedom than…
We consider the task of properly PAC learning decision trees with queries. Recent work of Koch, Strassle, and Tan showed that the strictest version of this task, where the hypothesis tree $T$ is required to be optimally small, is NP-hard.…
We study the fundamental problem of distributed network formation among mobile agents of limited computational power that aim to achieve energy balance by wirelessly transmitting and receiving energy in a peer-to-peer manner. Specifically,…
Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite…
This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties…
With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
We investigate the constraints on power flow in networks and its implications to the optimal power flow problem. The constraints are described by the injection region of a network; this is the set of all vectors of power injections, one at…
This paper proposes a novel approach using Graph Neural Networks (GNNs) to solve the AC Power Flow problem in power grids. AC OPF is essential for minimizing generation costs while meeting the operational constraints of the grid.…
A central issue in complex networks is tolerance to random failures and intentional attacks. Current literature emphasizes the dichotomy between networks with a power-law node connectivity distribution, which are robust to random failures…
The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach,…
When a flow is not allowed to be reoriented the Maximum Residual Flow Problem with $k$-Arc Destruction is known to be $NP$-hard for $k=2$. We show that when a flow is allowed to be adaptive the problem becomes polynomial for every fixed…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Given an undirected graph $G$ whose edge weights change over $s$ time slots, the sub-tree scheduling for wireless sensor networks with partial coverage asks to partition the vertices of $G$ in $s$ non-empty trees such that the total weight…
A widespread approach to characterise the aggregated flexibility of active distribution networks (ADNs) is to estimate the boundary of the feasible network operating areas using convex polygons in the P-Q space. However, such approximations…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow epsilon-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even when we allow $\epsilon$-contractions and add a reachability predicate (with regular constraints) for pairs of configurations, the structures…