Related papers: Graph colouring algorithms
A coloring of a graph G = (V,E) is a partition {V1, V2, . . ., Vk} of V into independent sets or color classes. A vertex v Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class Vj . A coloring is a Grundy…
We introduce learning augmented algorithms to the online graph coloring problem. Although the simple greedy algorithm FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of…
The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. For this NP-hard problem, a variety of integer linear…
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…
We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…
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…
The classic greedy coloring (first-fit) algorithm considers the vertices of an input graph $G$ in a given order and assigns the first available color to each vertex $v$ in $G$. In the {\sc Grundy Coloring} problem, the task is to find an…
Graph algorithms mainly belong to two categories, topology-driven and data-driven. Data-driven approach maintains a worklist of active nodes, the nodes on which work has to be done. Topology-driven approach sweeps over the entire graph to…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…
We provide a "how-to" guide to the use and application of the Discharging Method. Our aim is not to exhaustively survey results proved by this technique, but rather to demystify the technique and facilitate its wider use, using applications…
Graph machine learning has been extensively studied in both academia and industry. However, in the literature, most existing graph machine learning models are designed to conduct training with data samples in a random order, which may…
This paper explores the application of a new algebraic method of edge coloring, called complex coloring, to the scheduling problems of input queued switches. The proposed distributed parallel scheduling algorithm possesses two important…
Petford and Welsh introduced a sequential heuristic algorithm for (approximately) solving the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimics the behaviour of a physical process based on a…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…
This paper introduces the concept of domination in the context of colored graphs (where each color assigns a weight to the vertices of its class), termed up-color domination, where a vertex dominating another must be heavier than the other.…
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…
In this work, we present a branch-and-price algorithm to solve the weighted version of the List Coloring Problem, based on a vertex cover formulation by stable sets. This problem is interesting for its applications and also for the many…