SpecGreedy: Unified Dense Subgraph Detection

Efficient Directed Densest Subgraph Discovery

ACM SIGMOD Record ◽

10.1145/3471485.3471494 ◽

2021 ◽

Vol 50 (1) ◽

pp. 33-40

Author(s):

Chenhao Ma ◽

Yixiang Fang ◽

Reynold Cheng ◽

Laks V.S. Lakshmanan ◽

Wenjie Zhang ◽

...

Keyword(s):

Approximation Algorithms ◽

State Of The Art ◽

Exact Algorithms ◽

Large Datasets ◽

Dense Subgraph ◽

Extensive Evaluation ◽

Wide Range ◽

Edge Graph ◽

Community Mining ◽

Densest Subgraph

Given a directed graph G, the directed densest subgraph (DDS) problem refers to the finding of a subgraph from G, whose density is the highest among all the subgraphs of G. The DDS problem is fundamental to a wide range of applications, such as fraud detection, community mining, and graph compression. However, existing DDS solutions suffer from efficiency and scalability problems: on a threethousand- edge graph, it takes three days for one of the best exact algorithms to complete. In this paper, we develop an efficient and scalable DDS solution. We introduce the notion of [x, y]-core, which is a dense subgraph for G, and show that the densest subgraph can be accurately located through the [x, y]-core with theoretical guarantees. Based on the [x, y]-core, we develop both exact and approximation algorithms. We have performed an extensive evaluation of our approaches on eight real large datasets. The results show that our proposed solutions are up to six orders of magnitude faster than the state-of-the-art.

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Scalable mining of maximal quasi-cliques

Proceedings of the VLDB Endowment ◽

10.14778/3436905.3436916 ◽

2020 ◽

Vol 14 (4) ◽

pp. 573-585

Author(s):

Guimu Guo ◽

Da Yan ◽

M. Tamer Özsu ◽

Zhe Jiang ◽

Jalal Khalil

Keyword(s):

Graph Mining ◽

State Of The Art ◽

Minimum Degree ◽

The Other ◽

Dense Subgraph ◽

Load Imbalance ◽

Subgraph Mining ◽

Execution Engine ◽

Clique Algorithm ◽

Dense Subgraph Mining

Given a user-specified minimum degree threshold γ , a γ -quasiclique is a subgraph g = (V g , E g ) where each vertex ν ∈ V g connects to at least γ fraction of the other vertices (i.e., ⌈ γ · (| V g |- 1)⌉ vertices) in g. Quasi-clique is one of the most natural definitions for dense structures useful in finding communities in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive. In this paper, we design parallel algorithms for mining maximal quasi-cliques on G-thinker, a distributed graph mining framework that decomposes mining into compute-intensive tasks to fully utilize CPU cores. We found that directly using G-thinker results in the straggler problem due to (i) the drastic load imbalance among different tasks and (ii) the difficulty of predicting the task running time. We address these challenges by redesigning G-thinker's execution engine to prioritize long-running tasks for execution, and by utilizing a novel timeout strategy to effectively decompose long-running tasks to improve load balancing. While this system redesign applies to many other expensive dense subgraph mining problems, this paper verifies the idea by adapting the state-of-the-art quasi-clique algorithm, Quick, to our redesigned G-thinker. Extensive experiments verify that our new solution scales well with the number of CPU cores, achieving 201× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges in a 16-node cluster.

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Integration of dense subgraph finding with feature clustering for unsupervised feature selection

Pattern Recognition Letters ◽

10.1016/j.patrec.2013.12.008 ◽

2014 ◽

Vol 40 ◽

pp. 104-112 ◽

Cited By ~ 32

Author(s):

Sanghamitra Bandyopadhyay ◽

Tapas Bhadra ◽

Pabitra Mitra ◽

Ujjwal Maulik

Keyword(s):

Feature Selection ◽

Dense Subgraph ◽

Feature Clustering ◽

Unsupervised Feature Selection

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On Directed Densest Subgraph Discovery

ACM Transactions on Database Systems ◽

10.1145/3483940 ◽

2021 ◽

Vol 46 (4) ◽

pp. 1-45

Author(s):

Chenhao Ma ◽

Yixiang Fang ◽

Reynold Cheng ◽

Laks V. S. Lakshmanan ◽

Wenjie Zhang ◽

...

Keyword(s):

State Of The Art ◽

Directed Graphs ◽

Exact Algorithms ◽

Large Datasets ◽

Dense Subgraph ◽

Extensive Evaluation ◽

Wide Range ◽

Edge Graph ◽

Community Mining ◽

Densest Subgraph

Given a directed graph G , the directed densest subgraph (DDS) problem refers to the finding of a subgraph from G , whose density is the highest among all the subgraphs of G . The DDS problem is fundamental to a wide range of applications, such as fraud detection, community mining, and graph compression. However, existing DDS solutions suffer from efficiency and scalability problems: on a 3,000-edge graph, it takes three days for one of the best exact algorithms to complete. In this article, we develop an efficient and scalable DDS solution. We introduce the notion of [ x , y ]-core, which is a dense subgraph for G , and show that the densest subgraph can be accurately located through the [ x , y ]-core with theoretical guarantees. Based on the [ x , y ]-core, we develop exact and approximation algorithms. We further study the problems of maintaining the DDS over dynamic directed graphs and finding the weighted DDS on weighted directed graphs, and we develop efficient non-trivial algorithms to solve these two problems by extending our DDS algorithms. We have performed an extensive evaluation of our approaches on 15 real large datasets. The results show that our proposed solutions are up to six orders of magnitude faster than the state-of-the-art.

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