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The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…

Algebraic Geometry · Mathematics 2015-03-03 Tianran Chen , Dhagash Mehta

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…

Data Structures and Algorithms · Computer Science 2019-08-22 Laxman Dhulipala , Guy E. Blelloch , Julian Shun

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…

Data Structures and Algorithms · Computer Science 2012-11-15 Bharath Pattabiraman , Md. Mostofa Ali Patwary , Assefaw H. Gebremedhin , Wei-keng Liao , Alok Choudhary

In this paper, we investigate the problem of (k,r)-core which intends to find cohesive subgraphs on social networks considering both user engagement and similarity perspectives. In particular, we adopt the popular concept of k-core to…

Social and Information Networks · Computer Science 2016-11-11 Fan Zhang , Ying Zhang , Lu Qin , Wenjie Zhang , Xuemin Lin

Balanced butterfly counting, corresponding to counting balanced (2, 2)-bicliques, is a fundamental primitive in the analysis of signed bipartite graphs and provides a basis for studying higher-order structural properties such as clustering…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-27 Mekala Kiran , Apurba Das , Suman Banerjee , Tathagata Ray

Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…

Computational Complexity · Computer Science 2026-05-12 Nick Fischer , Marvin Künnemann , Mirza Redžić , Julian Stieß

This paper deals with the problem of finding, for a given graph and a given natural number k, a subgraph of k nodes with a maximum number of edges. This problem is known as the k-cluster problem and it is NP-hard on general graphs as well…

Data Structures and Algorithms · Computer Science 2011-11-09 George B. Mertzios

In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-02-18 Natalya Litvinenko

We address the problem of enumerating all temporal k-cores given a query time range and a temporal graph, which suffers from poor efficiency and scalability in the state-of-the-art solution. Motivated by an existing concept called core…

Databases · Computer Science 2025-08-21 Zhuo Ma , Dong Wen , Hanchen Wang , Wentao Li , Wenjie Zhang , Xuemin Lin

Clustering is an important tool in data analysis, with K-means being popular for its simplicity and versatility. However, it cannot handle non-linearly separable clusters. Kernel K-means addresses this limitation but requires a large kernel…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-29 Julian Bellavita , Matthew Rubino , Nakul Iyer , Andrew Chang , Aditya Devarakonda , Flavio Vella , Giulia Guidi

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…

Social and Information Networks · Computer Science 2013-12-30 Ryan A. Rossi , David F. Gleich , Assefaw H. Gebremedhin , Md. Mostofa Ali Patwary

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…

Discrete Mathematics · Computer Science 2007-10-04 Murali Krishna P , Sabu . M Thampi

Recent advances in graph processing on FPGAs promise to alleviate performance bottlenecks with irregular memory access patterns. Such bottlenecks challenge performance for a growing number of important application areas like machine…

Hardware Architecture · Computer Science 2022-06-20 Jonas Dann , Daniel Ritter , Holger Fröning

K Nearest Neighbor (KNN) joins are used in scientific domains for data analysis, and are building blocks of several well-known algorithms. KNN-joins find the KNN of all points in a dataset. This paper focuses on a hybrid CPU/GPU approach…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-11-19 Michael Gowanlock

Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-28 C Rashmi

Acceleration of graph applications on GPUs has found large interest due to the ubiquitous use of graph processing in various domains. The inherent \textit{irregularity} in graph applications leads to several challenges for parallelization.…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-11-02 Ananya Raval , Rupesh Nasre , Vivek Kumar , Vasudevan R , Sathish Vadhiyar , Keshav Pingali

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…

Data Structures and Algorithms · Computer Science 2014-12-01 Bharath Pattabiraman , Md. Mostofa Ali Patwary , Assefaw H. Gebremedhin , Wei-keng Liao , Alok Choudhary

The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…

Quantum Physics · Physics 2025-09-03 Wenmin Han , Shiqi Zheng , Peian Chen , Yukun Wang

Subgraph matching is a core operation in graph analytics, supporting a broad spectrum of applications from social network analysis to bioinformatics. Recent GPU-based approaches accelerate subgraph matching by leveraging parallelism but…

Databases · Computer Science 2026-04-14 Weitian Chen , Shixuan Sun , Cheng Chen , Yongmin Hu , Yingqian Hu , Minyi Guo

Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-07-24 Peter Sanders , Tim Niklas Uhl