Related papers: Collective dynamics of phase-repulsive oscillators…

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…

A classic graph coloring problem is to assign colors to vertices of any graph so that distinct colors are assigned to adjacent vertices. Optimal graph coloring colors a graph with a minimum number of colors, which is its chromatic number.…

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…

Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…

The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number…

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…

The field of descriptive combinatorics investigates the question, to what extent can classical combinatorial results and techniques be made topologically or measure-theoretically well-behaved? This paper examines a class of coloring…

In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…

We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…

We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. This is one of the most challenging problems in graph algorithms. In this paper using Blum's notion of ``progress'', we develop a…

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…

Neutral atom arrays have emerged as a versatile candidate for the embedding of hard classical optimization problems. Prior work has focused on mapping problems onto finding the maximum independent set of weighted or unweighted unit disk…

Asymptotic expansions of Gaussian integrals may often be interpreted as generating functions for certain combinatorial objects (graphs with additional data). In this article we discuss a general approach to all such cases using colored…

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…

Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…

Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…

We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the…

Dynamic optimization problems have gained significant attention in evolutionary computation as evolutionary algorithms (EAs) can easily adapt to changing environments. We show that EAs can solve the graph coloring problem for bipartite…