Related papers: Using Differential Evolution for the Graph Colorin…
Given a graph $G$ that is modified by a sequence of edge insertions and deletions, we study the Maximum $k$-Edge Coloring problem Having access to $k$ colors, how can we color as many edges of $G$ as possible such that no two adjacent edges…
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…
Graph neural networks have received increased attention over the past years due to their promising ability to handle graph-structured data, which can be found in many real-world problems such as recommended systems and drug synthesis. Most…
We consider a decentralized graph coloring model where each vertex only knows its own color and whether some neighbor has the same color as it. The networking community has studied this model extensively due to its applications to channel…
We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds. This answers one of the…
Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), it is still a challenging task to design an efficient binary-coded DE algorithm. Inspired by the learning mechanism of…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
A simple but empirically efficient heuristic algorithm for the edge-coloring of graphs is presented. Its basic idea is the displacement of "conflicts" (repeated colors in the edges incident to a vertex) along paths of adjacent vertices…
Evolutionary algorithms are metaheuristic techniques that derive inspiration from the natural process of evolution. They can efficiently solve (generate acceptable quality of solution in reasonable time) complex optimization (NP-Hard)…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
We present a polynomial-time algorithm that colors any 3-colorable $n$-vertex graph using $O(n^{0.19539})$ colors, improving upon the previous best bound of $\widetilde{O}(n^{0.19747})$ by Kawarabayashi, Thorup, and Yoneda [STOC 2024]. Our…
In the $\ell$-Coloring Problem, we are given a graph on $n$ nodes, and tasked with determining if its vertices can be properly colored using $\ell$ colors. In this paper we study below-guarantee graph coloring, which tests whether an…
DP-coloring (also called correspondence coloring) of graphs is a generalization of list coloring that has been widely studied since its introduction by Dvo\v{r}\'{a}k and Postle in $2015$. Intuitively, DP-coloring generalizes list coloring…
This paper explores the enhancement of solution diversity in evolutionary algorithms (EAs) for the maximum matching problem, concentrating on complete bipartite graphs and paths. We adopt binary string encoding for matchings and use Hamming…
We give a new, simple distributed algorithm for graph colouring in paths and cycles. Our algorithm is fast and self-contained, it does not need any globally consistent orientation, and it reduces the number of colours from $10^{100}$ to $3$…