Related papers: Graph reduction with spectral and cut guarantees
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random…
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic…
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Model repair is an essential topic in model-driven engineering. Since models are suitably formalized as graph-like structures, we consider the problem of rule-based graph repair: Given a rule set and a graph constraint, try to construct a…
Recent advances in machine learning (ML) have shown promise in aiding and accelerating classical combinatorial optimization algorithms. ML-based speed ups that aim to learn in an end to end manner (i.e., directly output the solution) tend…
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
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…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to biological and biomedical problems. The graph matching…
We initiate the study of spectral generalizations of the graph isomorphism problem. (a)The Spectral Graph Dominance (SGD) problem: On input of two graphs $G$ and $H$ does there exist a permutation $\pi$ such that $G\preceq \pi(H)$? (b) The…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
It is well-known [KST93] that the complexity of the Graph Automorphism problem is characterized by a special case of Graph Isomorphism, where the input graphs satisfy the "promise" of being rigid (that is, having no nontrivial…