Related papers: Distance-preserving graph contractions
A \emph{sparsification} of a given graph $G$ is a sparser graph (typically a subgraph) which aims to approximate or preserve some property of $G$. Examples of sparsifications include but are not limited to spanning trees, Steiner trees,…
In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal…
Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…
A sparsifier of a graph $G$ (Bencz\'ur and Karger; Spielman and Teng) is a sparse weighted subgraph $\tilde G$ that approximately retains the cut structure of $G$. For general graphs, non-trivial sparsification is possible only by using…
In this paper we consider the \emph{fully-dynamic} All-Pairs Effective Resistance problem, where the goal is to maintain effective resistances on a graph $G$ among any pair of query vertices under an intermixed sequence of edge insertions…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-edge…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
The performance and efficiency of distributed training of Deep Neural Networks highly depend on the performance of gradient averaging among all participating nodes, which is bounded by the communication between nodes. There are two major…
In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…
We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $\tau_\rho$, are there $k$ edges…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…