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While Boolean logic has been the backbone of digital information processing, there are classes of computationally hard problems wherein this conventional paradigm is fundamentally inefficient. Vertex coloring of graphs, belonging to the…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
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…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Several recent results from dynamic and sublinear graph coloring are surveyed. This problem is widely studied and has motivating applications like network topology control, constraint satisfaction, and real-time resource scheduling. Graph…
The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…
We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color to each node of a graph, in such a way that every pair of…
We study combinatorial indicators related to the characteristic phase transitions associated with coloring a graph optimally and finding a maximum independent set. In particular, we investigate the role of the acyclic orientations of the…
Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS,…
The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical…
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…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…
Differential evolution was developed for reliable and versatile function optimization. It has also become interesting for other domains because of its ease to use. In this paper, we posed the question of whether differential evolution can…
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations…