Related papers: Listing All Maximal Cliques in Large Sparse Real-W…
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph.…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
A new fast algorithm for clustering and classification of large collections of text documents is introduced. The new algorithm employs the bipartite graph that realizes the word-document matrix of the collection. Namely, the modularity of…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses.…
Mining dense subgraphs is an important primitive across a spectrum of graph-mining tasks. In this work, we formally establish that two recurring characteristics of real-world graphs, namely heavy-tailed degree distributions and large…
We conjecture that the worst case number of experiments necessary and sufficient to discover a causal graph uniquely given its observational Markov equivalence class can be specified as a function of the largest clique in the Markov…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
For a graph G=(V,E), finding a set of disjoint edges that do not share any vertices is called a matching problem, and finding the maximum matching is a fundamental problem in the theory of distributed graph algorithms. Although local…
A \emph{clique} is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with $n$ vertices and $m$ edges; (2) graphs with $n$ vertices, $m$ edges,…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
Kolla and Tulsiani [KT07,Kolla11} and Arora, Barak and Steurer [ABS10] introduced the technique of subspace enumeration, which gives approximation algorithms for graph problems such as unique games and small set expansion; the running time…
Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…