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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…
Graph coloring, a classical and critical NP-hard problem, is the problem of assigning connected nodes as different colors as possible. However, we observe that state-of-the-art GNNs are less successful in the graph coloring problem. We…
In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal…
We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
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…
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 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…
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…
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…
List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek many in parallel. Our explorations have uncovered a…
We consider the problem of online graph colouring. Whenever a node is requested, a colour must be assigned to the node, and this colour must be different from the colours of any of its neighbours. According to the greedy algorithm the node…
Approximate random $k$-colouring of a graph $G$ is a well studied problem in computer science and statistical physics. It amounts to constructing a $k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in polynomial…
We study the maximization version of the fundamental graph coloring problem. Here the goal is to color the vertices of a k-colorable graph with k colors so that a maximum fraction of edges are properly colored (i.e. their endpoints receive…
We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning,…
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…