Related papers: Graph Coloring Using Heat Diffusion
We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different…
Unsupervised plain graph alignment (UPGA) aims to align corresponding nodes across two graphs without any auxiliary information. Existing UPGA methods rely on structural consistency while neglecting the inherent structural differences in…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Graph Coloring consists in assigning colors to vertices ensuring that two adjacent vertices do not have the same color. In dynamic graphs, this notion is not well defined, as we need to decide if different colors for adjacent vertices must…
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we…
Graph coloring has been broadly used to discover concurrency in parallel computing. To speedup graph coloring for large-scale datasets, parallel algorithms have been proposed to leverage modern GPUs. Existing GPU implementations either have…
Hypergraphs are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
We observe a network scenario where parts of a secret are distributed among its nodes. Within the network, a group of attackers is actively trying to obtain the complete secret, while there is also the issue of some nodes malfunctioning or…