Local algorithms for hierarchical dense subgraph discovery

Author:

Sariyüce Ahmet Erdem1,Seshadhri C.2,Pinar Ali3

Affiliation:

1. University at Buffalo Buffalo

2. University of California Santa Cruz

3. Sandia National Laboratories Livermore

Abstract

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 these decompositions and the need for global information at each step of the algorithm hinders scalable parallelization and approximations since the densest regions are not revealed until the end. In a previous work, Lu et al. proposed to iteratively compute the h -indices of neighbor vertex degrees to obtain the core numbers and prove that the convergence is obtained after a finite number of iterations. This work generalizes the iterative h -index computation for truss decomposition as well as nucleus decomposition which leverages higher-order structures to generalize core and truss decompositions. In addition, we prove convergence bounds on the number of iterations. We present a framework of local algorithms to obtain the core, truss, and nucleus decompositions. Our algorithms are local, parallel, offer high scalability, and enable approximations to explore time and quality trade-offs. Our shared-memory implementation verifies the efficiency, scalability, and effectiveness of our local algorithms on real-world networks.

Publisher

VLDB Endowment

Subject

General Earth and Planetary Sciences,Water Science and Technology,Geography, Planning and Development

Cited by 51 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Efficient Algorithms for Density Decomposition on Large Static and Dynamic Graphs;Proceedings of the VLDB Endowment;2024-07

2. MCR-Tree: An Efficient Index for Multi-dimensional Core Search;Proceedings of the ACM on Management of Data;2024-05-29

3. A Counting-based Approach for Efficient k-Clique Densest Subgraph Discovery;Proceedings of the ACM on Management of Data;2024-05-29

4. Fast Multilayer Core Decomposition and Indexing;2024 IEEE 40th International Conference on Data Engineering (ICDE);2024-05-13

5. Efficient Core Decomposition Over Large Heterogeneous Information Networks;2024 IEEE 40th International Conference on Data Engineering (ICDE);2024-05-13

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