Related papers: The Power Contamination Problem on Grids Revisited…
Given a graph $G$, the optimization version of the graph burning problem seeks for a sequence of vertices, $(u_1,u_2,...,u_p) \in V(G)^p$, with minimum $p$ and such that every $v \in V(G)$ has distance at most $p-i$ to some vertex $u_i$.…
Optimization-based power control algorithms are predominantly iterative with high computational complexity, making them impractical for real-time applications in cell-free massive multiple-input multiple-output (CFmMIMO) systems.…
This paper aims to identify and analyze the initial contingencies or disturbances that could lead to the worst-case cascading failures of power grids. An optimal control approach is proposed to determine the most disruptive disturbances on…
From the perspective of global warming, efficiency improvement of power grids is a pressing issue. Power grids have many switching devices to control the flow of electricity. Since there is a slight resistance in the wires and power…
A power dominating set of a graph is a set of vertices that observes every vertex in the graph by combining classical domination with an iterative propagation process arising from electrical circuit theory. In this paper, we study the power…
In this work, we study the problem of clearing contamination spreading through a large network where we model the problem as a graph searching game. The problem can be summarized as constructing a search strategy that will leave the graph…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
The power domination number arises from the monitoring of electrical networks and its determination is an important problem. Upper bounds for power domination numbers can be obtained by constructions. Lower bounds for the power domination…
As graph data becomes more ubiquitous, the need for robust inferential graph algorithms to operate in these complex data domains is crucial. In many cases of interest, inference is further complicated by the presence of adversarial data…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
Our goal is to prove new results in graph theory and combinatorics thanks to the speed of computers, used with smart algorithms. We tackle four problems. The four-colour theorem states that any map whose countries are connected can be…
The problem of partitioning a power grid into a set of islands can be a solution to restore power dispatchment in sections of a grid affected by an extreme failure. Current solutions to this problem usually involve finding the partition of…
The domination number of a graph $G = (V,E)$ is the minimum cardinality of any subset $S \subset V$ such that every vertex in $V$ is in $S$ or adjacent to an element of $S$. Finding the domination numbers of $m$ by $n$ grids was an open…
In this report, we consider maximal solutions to the induced bounded-degree subgraph problem and relate it to issues concerning stream control in multiple-input multiple-output (MIMO) networks. We present a new distributed algorithm that…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient…
The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S $\subseteq$ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…
The collection of all the strongly connected components in a directed graph, among each cluster of which any node has a path to another node, is a typical example of the intertwining structure and dynamics in complex networks, as its…