Top-k overlapping densest subgraphs

Galbrun, Esther; Gionis, Aristides; Tatti, Nikolaj

doi:10.1007/s10618-016-0464-z

Cited by 56 publications

(60 citation statements)

References 38 publications

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“…Exact algorithms [14], [15] and approximate algorithms [10], [15] have been proposed for finding subgraphs with maximum average degree. These have been extended for incorporating size restrictions [27], alternative metrics for denser subgraphs [13], evolving graphs [28], subgraphs with limited overlap [29], [30], and streaming or distributed settings [31], [32]. Dense subgraph detection has been applied to fraud detection in social or review networks [5], [12], [33], [34], [35].…”

Section: Related Workmentioning

confidence: 99%

Fast, Accurate, and Flexible Algorithms for Dense Subtensor Mining

Shin

Hooi

Faloutsos

2018

ACM Trans. Knowl. Discov. Data

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How can we detect fraudulent lockstep behavior in large-scale multi-aspect data (i.e., tensors)? Can we detect it when data are too large to fit in memory or even on a disk? Past studies have shown that dense subtensors in real-world tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or fraudulent behavior such as retweet boosting, bot activities, and network attacks. Thus, various approaches, including tensor decomposition and search, have been proposed for detecting dense subtensors rapidly and accurately. However, existing methods have low accuracy, or they assume that tensors are small enough to fit in main memory, which is unrealistic in many real-world applications such as social media and web. To overcome these limitations, we propose D-CUBE, a disk-based dense-subtensor detection method, which also can run in a distributed manner across multiple machines. Compared to state-of-the-art methods, D-CUBE is (1) Memory Efficient: requires up to 1,600× less memory and handles 1,000× larger data (2.6TB), (2) Fast: up to 7× faster due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on the densities of the detected subtensors, and (4) Effective: spotted network attacks from TCP dumps and synchronized behavior in rating data most accurately.

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Section: Related Workmentioning

confidence: 99%

Fast, Accurate, and Flexible Algorithms for Dense Subtensor Mining

Shin

Hooi

Faloutsos

2018

ACM Trans. Knowl. Discov. Data

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“…In many real applications, the objective is to find a set of cohesive subgraphs of the original input graph (rather than a single subgraph covering the input). Following the approach proposed in [11], this paper considers the problem of computing the set of largest k 2-clubs, with k ≥ 1. We will denote this problem as Top k-2-clubs.…”

Section: Iccs Camera Ready Version 2019mentioning

confidence: 99%

Top k 2-Clubs in a Network: A Genetic Algorithm

Castelli

Dondi

Manzoni

et al. 2019

Lecture Notes in Computer Science

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The identification of cohesive communities (dense subgraphs) is a typical task applied to the analysis of social and biological networks. Different definitions of communities have been adopted for particular occurrences. One of these, the 2-club (dense subgraphs with diameter value at most of length 2) has been revealed of interest for applications and theoretical studies. Unfortunately, the identification of 2-clubs is a computationally intractable problem, and the search of approximate solutions (at a reasonable time) is therefore fundamental in many practical areas. In this article, we present a genetic algorithm based heuristic to compute a collection of Top k 2-clubs, i.e., a set composed by the largest k 2-clubs which cover an input graph. In particular, we discuss some preliminary results for synthetic data obtained by sampling Erdös-Rényi random graphs.

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“…e problem of nding the top-k densest subgraph as sum of densities was shown to be NP-hard [6] and e cient heuristic was proposed to solve the problem. Further, Galbrun et al [17] studied the problem of nding the top-k overlapping densest subgraphs and provided constant-factor approximation guarantees.…”

Section: Related Workmentioning

confidence: 99%

“…In applications, we are o en interested not only in one densest subgraph, but in the top-k. e top-k densest subgraphs can be vertex-disjoint, edge-disjoint, or overlapping [6,17]. Di erent objective functions and constraints give rise to di erent problem formulations [6,17,32]. In this work, we choose to maximize the sum of the densities of the k subgraphs in the solution.…”

Section: Introductionmentioning

confidence: 99%

Fully Dynamic Algorithm for Top- k Densest Subgraphs

Nasir

Gionis

Morales

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

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Given a large graph, the densest-subgraph problem asks to nd a subgraph with maximum average degree. When considering the top-k version of this problem, a naïve solution is to iteratively nd the densest subgraph and remove it in each iteration. However, such a solution is impractical due to high processing cost. e problem is further complicated when dealing with dynamic graphs, since adding or removing an edge requires re-running the algorithm. In this paper, we study the top-k densest-subgraph problem in the sliding-window model and propose an e cient fully-dynamic algorithm. e input of our algorithm consists of an edge stream, and the goal is to nd the node-disjoint subgraphs that maximize the sum of their densities. In contrast to existing state-of-the-art solutions that require iterating over the entire graph upon any update, our algorithm pro ts from the observation that updates only a ect a limited region of the graph. erefore, the top-k densest subgraphs are maintained by only applying local updates. We provide a theoretical analysis of the proposed algorithm and show empirically that the algorithm o en generates denser subgraphs than state-of-the-art competitors. Experiments show an improvement in e ciency of up to ve orders of magnitude compared to state-of-the-art solutions.

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Top-k overlapping densest subgraphs

Cited by 56 publications

References 38 publications

Fast, Accurate, and Flexible Algorithms for Dense Subtensor Mining

Fast, Accurate, and Flexible Algorithms for Dense Subtensor Mining

Top k 2-Clubs in a Network: A Genetic Algorithm

Fully Dynamic Algorithm for Top- k Densest Subgraphs

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