Related papers: Tree-based Coarsening and Partitioning of Complex …
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
Graph convolutional networks (GCNs) are nowadays becoming mainstream in solving many image processing tasks including skeleton-based recognition. Their general recipe consists in learning convolutional and attention layers that maximize…
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools.…
Let be given a graph $G=(V,E)$ whose edge set is partitioned into a set $R$ of \emph{red} edges and a set $B$ of \emph{blue} edges, and assume that red edges are weighted and form a spanning tree of $G$. Then, the \emph{Stackelberg Minimum…
We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph $G$ and integers $k,x \ge 0$, Critical Node Cut (CNC) asks whether we can delete at most $k$ vertices so that the number of remaining unordered…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
A novel method to identify salient computational paths within randomly wired neural networks before training is proposed. The computational graph is pruned based on a node mass probability function defined by local graph measures and…
Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…
We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem,…
How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…
Graph edge partitioning is an important preprocessing step to optimize distributed computing jobs on graph-structured data. The edge set of a given graph is split into $k$ equally-sized partitions, such that the replication of vertices…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then…
We present a multi-level graph partitioning algorithm based on the extreme idea to contract only a single edge on each level of the hierarchy. This obviates the need for a matching algorithm and promises very good partitioning quality since…
In the problem (Unweighted) Max-Cut we are given a graph $G = (V,E)$ and asked for a set $S \subseteq V$ such that the number of edges from $S$ to $V \setminus S$ is maximal. In this paper we consider an even harder problem: (Weighted)…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…
Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…