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Deep networks have shown impressive performance in the image restoration tasks, such as image colorization. However, we find that previous approaches rely on the digital representation from single color model with a specific mapping…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
Graph deep learning methods have become popular tools to process collections of correlated time series. Unlike traditional multivariate forecasting methods, graph-based predictors leverage pairwise relationships by conditioning forecasts on…
In this paper, we present a novel approach that uses deep learning techniques for colorizing grayscale images. By utilizing a pre-trained convolutional neural network, which is originally designed for image classification, we are able to…
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
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…
We consider coloring problems in the distributed message-passing setting. The previously-known deterministic algorithms for edge-coloring employed at least (2Delta - 1) colors, even though any graph admits an edge-coloring with Delta + 1…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
We study a graph coloring problem that is otherwise easy but becomes quite non-trivial in the one-pass streaming model. In contrast to previous graph coloring problems in streaming that try to find an assignment of colors to vertices, our…
In the Selective Coloring problem, we are given an integer $k$, a graph $G$, and a partition of $V(G)$ into $p$ parts, and the goal is to decide whether or not we can pick exactly one vertex of each part and obtain a $k$-colorable induced…
In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is…
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…
In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph…
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…
In recent years, machine learning and deep learning approaches such as artificial neural networks have gained in popularity for the resolution of automatic puzzle resolution problems. Indeed, these methods are able to extract high-level…
Vizing's theorem states that any graph of maximum degree $\Delta$ can be properly edge colored with at most $\Delta+1$ colors. In the online setting, it has been a matter of interest to find an algorithm that can properly edge color any…
A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as…
Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for…