Related papers: Coloring Large Complex Networks
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the…
We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design…
We explore the interplay between architectures and algorithm design in the context of shared-memory platforms and a specific graph problem of central importance in scientific and high-performance computing, distance-1 graph coloring. We…
In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
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…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
Community detection in social graphs has attracted researchers' interest for a long time. With the widespread of social networks on the Internet it has recently become an important research domain. Most contributions focus upon the…
Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
Narrow sieves, representative sets and divide-and-color are three breakthrough color coding-related techniques, which led to the design of extremely fast parameterized algorithms. We present a novel family of strategies for applying…
The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most…
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…
We consider the maximum chromatic number of hypergraphs consisting of cliques that have pairwise small intersections. Designs of the appropriate parameters produce optimal constructions, but these are known to exist only when the number of…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
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…