Bitruss Decomposition of Bipartite Graphs

Zou, Zhaonian

doi:10.1007/978-3-319-32049-6_14

Cited by 51 publications

(39 citation statements)

References 12 publications

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“…In [4], the authors combine the influence property with (α, β)-core for community detection. Considering the structure properties, Zou et al [9] propose the bitruss model, where each edge in the community is contained in at least k butterflies. To further study the clustering ability in bipartite graphs, Flajolet et al [27] use the ratio of the number of butterflies to the number of three paths for modeling the cohesiveness of the graph.…”

Section: Related Workmentioning

confidence: 99%

“…As a fundamental problem in graph analysis, cohesive subgraph identification is widely studied in the literature (e.g., [5][6][7][8]). For bipartite graphs, a variety of cohesive subgraph models have been proposed to identify important structures, such as (α, β)core [3], bitruss [9] and biclique [10]. Biclique is the most cohesive model, which requires the nodes inside to be fully connected.…”

Section: Introductionmentioning

confidence: 99%

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Cohesive Subgraph Identification in Weighted Bipartite Graphs

Liu

Wang

2021

Applied Sciences

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Cohesive subgraph identification is a fundamental problem in bipartite graph analysis. In real applications, to better represent the co-relationship between entities, edges are usually associated with weights or frequencies, which are neglected by most existing research. To fill the gap, we propose a new cohesive subgraph model, (k,ω)-core, by considering both subgraph cohesiveness and frequency for weighted bipartite graphs. Specifically, (k,ω)-core requires each node on the left layer to have at least k neighbors (cohesiveness) and each node on the right layer to have a weight of at least ω (frequency). In real scenarios, different users may have different parameter requirements. To handle massive graphs and queries, index-based strategies are developed. In addition, effective optimization techniques are proposed to improve the index construction phase. Compared with the baseline, extensive experiments on six datasets validate the superiority of our proposed methods.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cohesive Subgraph Identification in Weighted Bipartite Graphs

Liu

Wang

2021

Applied Sciences

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“…Unlike other near-clique substructures like 𝑘-plexes, 𝑛-clans, and 𝑛-clubs, which are computationally intractable to enumerate and count, 𝑘-trusses can be efficiently found in polynomial-time. Many parallel, external-memory, and distributed algorithms have been developed in the past decade for 𝑘-cores [20,25,35,37,49,70] and 𝑘-trusses [7,12,13,17,36,44,62,67,75], and computing all trussness values of a graph is one of the challenge problems in the yearly MIT GraphChallenge [50]. A related problem is to compute the 𝑘-clique densest subgraph [65] and (𝑘, Ψ)core [24], for which efficient parallel algorithms have been recently designed [59].…”

Section: Related Workmentioning

confidence: 99%

Theoretically and Practically Efficient Parallel Nucleus Decomposition

Shi

Dhulipala

Shun

2021

Preprint

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This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves a work complexity matching the best sequential algorithm while also having low depth (parallel running time), which significantly improves upon the only existing parallel nucleus decomposition algorithm (Sariyüce et al., PVLDB 2018). The key to the theoretical efficiency of our algorithm is a new lemma that bounds the amount of work done when peeling cliques from the graph, combined with the use of a theoretically-efficient parallel algorithms for clique listing and bucketing. We introduce several new practical optimizations, including a new multi-level hash table structure to store information on cliques space-efficiently and a technique for traversing this structure cache-efficiently. On a 30-core machine with two-way hyper-threading on real-world graphs, we achieve up to a 55x speedup over the state-of-the-art parallel nucleus decomposition algorithm by Sariyüce et al., and up to a 40x self-relative parallel speedup. We are able to efficiently compute larger nucleus decompositions than prior work on several million-scale graphs for the first time.

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“…Similar to nucleus decomposition algorithms, they designed bottom-up peeling algorithms to find hierarchies of 𝑘-tips and 𝑘-wings. Independently, Zou [72] defined the notion of bitruss similar to 𝑘-wing. Shi et al [54] propose the 𝑃ar𝐵utterfly framework that parallelizes individual peeling iterations.…”

Section: Related Workmentioning

confidence: 99%

“…Several real-world systems naturally exhibit bipartite relationships, such as consumer-product purchase network of an e-commerce website [26], user-ratings data in a recommendation system [23,34], author-paper network of a scientific field [41], group memberships in a social network [37] etc. Due to the rapid growth of data produced in these domains, efficient mining of dense structures in bipartite graphs has become a popular research topic [30,51,54,66,67,72].…”

Section: Introductionmentioning

confidence: 99%

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

Lakhotia¹,

Kannan²,

Prasanna³

2021

Preprint

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Motif-based graph decomposition is widely used to mine hierarchical dense structures in graphs. In bipartite graphs, wing and tip decomposition construct a hierarchy of butterfly (2,2-biclique) dense edge and vertex induced subgraphs, respectively. They have applications in several domains including e-commerce, recommendation systems and document analysis.Existing decomposition algorithms use a bottom-up approach that constructs the hierarchy in an increasing order of subgraph density. They iteratively select the entities (edges or vertices) with minimum support (butterfly count) and peel them i.e. remove them from them graph and update the support of other entities. The amount of butterflies in real-world bipartite graphs makes bottom-up peeling computationally demanding. Furthermore, the strict order of peeling entities results in a large number of iterations with sequential dependencies on preceding support updates. Consequently, parallel algorithms based on bottom up peeling can only utilize intra-iteration parallelism and require heavy synchronization, leading to poor scalability.In this paper, we propose a novel Parallel Bipartite Network peelinG (PBNG) framework which adopts a two-phased peeling approach to relax the order of peeling, and in turn, dramatically reduce synchronization. The first phase divides the decomposition hierarchy into few partitions, and requires little synchronization to compute such partitioning. The second phase concurrently processes all of these partitions to generate individual levels in the final decomposition hierarchy, and requires no global synchronization.Effectively, both phases of PBNG parallelize computation across multiple levels of decomposition hierarchy, which is not possible with bottom-up peeling. The two-phased peeling further enables batching optimizations that dramatically improve the computational efficiency of PBNG. The proposed approach represents a non-trivial generalization of our prior work on a two-phased vertex peeling algorithm [30], and its adoption for both tip and wing decomposition.We empirically evaluate PBNG using several real-world bipartite graphs and demonstrate radical improvements over the existing approaches. On a shared-memory 36 core server, PBNG achieves up to 19.7× self-relative parallel speedup. Compared to the state-of-theart parallel framework ParButterfly, PBNG reduces synchronization by up to 15260× and execution time by up to 295×. Furthermore, it achieves up to 38.5× speedup over state-of-the-art algorithms specifically tuned for wing decomposition. We also present the first decomposition results of some of the largest public real-world datasets, which PBNG can peel in few minutes/hours, but algorithms in current practice fail to process even in several days. Our source code is made available at https://github.com/kartiklakhotia/RECEIPT.

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Bitruss Decomposition of Bipartite Graphs

Cited by 51 publications

References 12 publications

Cohesive Subgraph Identification in Weighted Bipartite Graphs

Cohesive Subgraph Identification in Weighted Bipartite Graphs

Theoretically and Practically Efficient Parallel Nucleus Decomposition

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

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