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We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
A coloring of edges of a finite directed graph turns the graph into finite-state automaton. The synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton…
We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time…
In this paper, we present improved algorithms for the $(\Delta+1)$ (vertex) coloring problem in the Congested-Clique model of distributed computing. In this model, the input is a graph on $n$ nodes, initially each node knows only its…
Given a graph $G$ with $n$ vertices and maximum degree $\Delta$, it is known that $G$ admits a vertex coloring with $\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm,…
We present ${\rm poly\log\log n}$-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into $k$ parts such that a node of degree $d(u)$ has $\approx d(u)/k$ neighbors in each part. Our…
Clique-width is a complexity measure of directed as well as undirected graphs. Rank-width is an equivalent complexity measure for undirected graphs and has good algorithmic and structural properties. It is in particular related to the…
Graph Anomaly Detection (GAD) has recently become a hot research spot due to its practicability and theoretical value. Since GAD emphasizes the application and the rarity of anomalous samples, enriching the varieties of its datasets is…
Deep neural networks for automatic image colorization often suffer from the color-bleeding artifact, a problematic color spreading near the boundaries between adjacent objects. Such color-bleeding artifacts debase the reality of generated…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…
We propose an effective algorithm that enumerates (and actually finds) all 3-edge colorings and Hamiltonian cycles in a cubic graph. The idea is to make a preliminary run that separates the vertices into two types: ``rigid'' (such that the…
Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…
Answer Set Programming (ASP) is a famous logic language for knowledge representation, which has been really successful in the last years, as witnessed by the great interest into the development of efficient solvers for ASP. Yet, the great…
Given a dynamic graph $G$ with $n$ vertices and $m$ edges subject to insertion an deletions of edges, we show how to maintain a $(1+\varepsilon)\Delta$-edge-colouring of $G$ without the use of randomisation. More specifically, we show a…
Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…
This paper presents massively parallel computation (MPC) algorithms in the strongly sublinear memory regime (aka, scalable MPC) for orienting and coloring graphs as a function of its subgraph density. Our algorithms run in $poly(\log\log…
In-context learning (ICL) enhances large language models (LLMs) by incorporating demonstration examples, yet its effectiveness heavily depends on the quality of selected examples. Current methods typically use text embeddings to measure…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised…
Network alignment (NA) is the task of finding the correspondence of nodes between two networks based on the network structure and node attributes. Our study is motivated by the fact that, since most of existing NA methods have attempted to…
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,…