Related papers: Graph Spanners in the Message-Passing Model
Graph Neural Networks (GNNs) are powerful and flexible neural networks that use the naturally sparse connectivity information of the data. GNNs represent this connectivity as sparse matrices, which have lower arithmetic intensity and thus…
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…
Message passing neural networks have recently evolved into a state-of-the-art approach to representation learning on graphs. Existing methods perform synchronous message passing along all edges in multiple subsequent rounds and consequently…
The message passing framework is the foundation of the immense success enjoyed by graph neural networks (GNNs) in recent years. In spite of its elegance, there exist many problems it provably cannot solve over given input graphs. This has…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse…
Graph Neural Networks (GNNs) are a computationally efficient method to learn embeddings and classifications on graph data. However, GNN training has low computational intensity, making communication costs the bottleneck for scalability.…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Graph Neural Networks (GNNs) have been proposed as a tool for learning sparse matrix preconditioners, which are key components in accelerating linear solvers. We present theoretical and empirical evidence that message-passing GNNs are…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Given a connected graph $G=(V,E)$ and a length function $\ell:E\to {\mathbb R}$ we let $d_{v,w}$ denote the shortest distance between vertex $v$ and vertex $w$. A $t$-spanner is a subset $E'\subseteq E$ such that if $d'_{v,w}$ denotes…
Graph neural networks (GNNs) based on message passing between neighboring nodes are known to be insufficient for capturing long-range interactions in graphs. In this project we study hierarchical message passing models that leverage a…
Given a metric space $\mathcal{M}=(X,\delta)$, a weighted graph $G$ over $X$ is a metric $t$-spanner of $\mathcal{M}$ if for every $u,v \in X$, $\delta(u,v)\le d_G(u,v)\le t\cdot \delta(u,v)$, where $d_G$ is the shortest path metric in $G$.…
Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…
A sparse graph that preserves an approximation of the shortest paths between all pairs of points in a plane is called a geometric spanner. Using range trees of sublinear size, we design an algorithm in massively parallel computation (MPC)…
Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…
Subgraph isomorphism counting is an important problem on graphs, as many graph-based tasks exploit recurring subgraph patterns. Classical methods usually boil down to a backtracking framework that needs to navigate a huge search space with…