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The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…

The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions.…

Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…

We study the problem of efficient, scalable set-sharing analysis of logic programs. We use the idea of representing sharing information as a pair of abstract substitutions, one of which is a worst-case sharing representation called a clique…

We study the planted clique problem in which a clique of size k is planted in an Erdos-Renyi graph G(n,1/2) and one is interested in recovering this planted clique. It is widely believed that it exhibits a statistical-computational gap when…

Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…

Inference problems with conjectured statistical-computational gaps are ubiquitous throughout modern statistics, computer science and statistical physics. While there has been success evidencing these gaps from the failure of restricted…

Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles…

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…

The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…

Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…

Consider an Erd\"os-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely connected subgraph). We consider the problem of…

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…

A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…

Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…

K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…