Related papers: On Distributed Colouring of Hyperbolic Random Grap…
Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…
We consider the problem of coloring graphs of maximum degree $\Delta$ with $\Delta$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model.…
For a given graph $H$ we define $\rho(H)$ to be the minimum order of a graph $G$ such that every proper vertex coloring of $G$ contains a rainbow induced subgraph isomorphic to $H$. We give upper and lower bounds for $\rho(H)$, compute the…
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…
The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
In distributed network computing, a variant of the LOCAL model has been recently introduced, referred to as the SLEEPING model. In this model, nodes have the ability to decide on which round they are awake, and on which round they are…
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…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs of $G$ is referred to as a (random) {\sl perturbation} of $G$. We consider the…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of…
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…
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…
One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are…
A simple but empirically efficient heuristic algorithm for the edge-coloring of graphs is presented. Its basic idea is the displacement of "conflicts" (repeated colors in the edges incident to a vertex) along paths of adjacent vertices…
Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing…
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…
Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden…