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A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…

Data Structures and Algorithms · Computer Science 2024-07-25 Chunyu Luo , Yi Zhou , Zhengren Wang , Mingyu Xiao

We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…

Data Structures and Algorithms · Computer Science 2021-07-19 Jessica Shi , Laxman Dhulipala , Julian Shun

Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…

Data Structures and Algorithms · Computer Science 2017-12-11 Panagiotis Strouthopoulos , Apostolos Papadopoulos

Distributed Compressive Sensing (DCS) improves the signal recovery performance of multi signal ensembles by exploiting both intra- and inter-signal correlation and sparsity structure. However, the existing DCS was proposed for a very…

Information Theory · Computer Science 2012-11-29 Jeonghun Park , Seunggye Hwang , Janghoon Yang , Dongku Kim

Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core…

Machine Learning · Statistics 2023-03-29 Yang Guo , Xuekui Zhang , Fatemeh Esfahani , Venkatesh Srinivasan , Alex Thomo , Li Xing

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-01-23 Jessica Shi , Laxman Dhulipala , Julian Shun

Given a query graph that represents a pattern of interest, the emerging pattern detection problem can be viewed as a continuous query problem on a dynamic graph. We present an incremental algorithm for continuous query processing on dynamic…

Databases · Computer Science 2014-07-15 Sutanay Choudhury , Lawrence Holder , George Chin , Patrick Mackey , Khushbu Agarwal , John Feo

Most applications demand high-performance deep neural architectures costing limited resources. Neural architecture searching is a way of automatically exploring optimal deep neural networks in a given huge search space. However, all…

Machine Learning · Computer Science 2020-06-01 Yunhe Wang , Yixing Xu , Dacheng Tao

Finding dense subgraphs of a large network is a fundamental problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications over the last five decades. However, most existing…

Social and Information Networks · Computer Science 2023-10-10 Ali Behrouz , Farnoosh Hashemi

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

Data Structures and Algorithms · Computer Science 2021-06-07 Nate Veldt , Austin R. Benson , Jon Kleinberg

As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…

Data Structures and Algorithms · Computer Science 2018-12-31 Sepehr Assadi , MohammadHossein Bateni , Aaron Bernstein , Vahab Mirrokni , Cliff Stein

Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…

Databases · Computer Science 2023-08-29 Kaiqiang Yu , Cheng Long

Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes…

Data Structures and Algorithms · Computer Science 2014-05-22 Charalampos E. Tsourakakis

In this paper, we present a collection of novel and scalable algorithms designed to tackle the challenges inherent in the $k$-clique densest subgraph problem (\kcdsp) within network analysis. We propose \psctl, a novel algorithm based on…

Data Structures and Algorithms · Computer Science 2024-03-12 Xiaowei Ye , Miao Qiao , Rong-Hua Li , Qi Zhang , Guoren Wang

Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…

Data Structures and Algorithms · Computer Science 2011-12-12 Robert Görke , Andrea Schumm , Dorothea Wagner

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the…

Data Structures and Algorithms · Computer Science 2024-06-05 Dung Nguyen , Anil Vullikanti

Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…

Social and Information Networks · Computer Science 2018-09-17 Ahmet Erdem Sariyuce , C. Seshadhri , Ali Pinar

Given a graph $G$ and a vertex $q\in G$, the community search (CS) problem aims to efficiently find a subgraph of $G$ whose vertices are closely related to $q$. Communities are prevalent in social and biological networks, and can be used in…

Databases · Computer Science 2019-01-18 Yankai Chen , Yixiang Fang , Reynold Cheng , Yun Li , Xiaojun Chen , Jie Zhang

Decomposing hypergraphs is a key task in hypergraph analysis with broad applications in community detection, pattern discovery, and task scheduling. Existing approaches such as $k$-core and neighbor-$k$-core rely on vertex degree…

Social and Information Networks · Computer Science 2026-04-10 Xiaoyu Leng , Hongchao Qin , Rong-Hua Li

Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…

Optimization and Control · Mathematics 2021-09-03 Alexander Engelmann , Timm Faulwasser