Local algorithms for hierarchical dense subgraph discovery

Sarıyüce, Ahmet Erdem; Seshadhri, C.; Pınar, Ali

doi:10.14778/3275536.3275540

Cited by 61 publications

(35 citation statements)

References 45 publications

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“…Our sequential bounds are asymptotically better than theirs in terms of either work or space, except in the highly degenerate case where C(G, k) = o(ρ log n). Sariyuce et al [47] also give a parallel algorithm, which is similarly not work-efficient.…”

Section: Vertex Peelingmentioning

confidence: 99%

Parallel Clique Counting and Peeling Algorithms

Shi¹,

Dhulipala²,

Shun³

2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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We present a new parallel algorithm for k-clique counting/listing that has polylogarithmic span (parallel time) and is workefficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on computing low out-degree orientations, which we present new linear-work and polylogarithmic-span algorithms for computing in parallel. We also present new parallel algorithms for producing unbiased estimations of clique counts using graph sparsification. Finally, we design two new parallel work-efficient algorithms for approximating the k-clique densest subgraph, the first of which is a 1/k-approximation and the second of which is a 1/(k(1 + ))-approximation and has polylogarithmic span. Our first algorithm does not have polylogarithmic span, but we prove that it solves a P-complete problem.In addition to the theoretical results, we also implement the algorithms and propose various optimizations to improve their practical performance. On a 30-core machine with two-way hyper-threading, our algorithms achieve 13.23-38.99x and 1.19-13.76x self-relative parallel speedup for k-clique counting and k-clique densest subgraph, respectively. Compared to the state-of-the-art parallel k-clique counting algorithms, we achieve up to 9.88x speedup, and compared to existing implementations of k-clique densest subgraph, we achieve up to 11.83x speedup. We are able to compute the 4-clique counts on the largest publicly-available graph with over two hundred billion edges for the first time.

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Section: Vertex Peelingmentioning

confidence: 99%

Parallel Clique Counting and Peeling Algorithms

Shi¹,

Dhulipala²,

Shun³

2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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“…As we have presented in Section 2, the nucleous decomposition is a framework that generalizes the k-core and k-truss decompositions, using higher order structures to find dense subgraphs. The authors of [129] generalized the work by Lu et al for any nucleus decomposition -providing also theoretical quarantess about the convergence properties. In addition, the proposed algorithms are highly parallel due to the fact that they operate based on local computations.…”

Section: Local Computation Of Core Numbersmentioning

confidence: 96%

“…Truss and nucleus decomposition. In a more recent work, Sariyüce et al [129] capitalized on the relationship between core number and h-index [98], in order to propose efficient local algorithms for truss and nucleus decomposition with convergence guarantees. Lu et al [98] have introduced an alternative formulation for the k-core decomposition that considers local information, utilizing the concept of h-index which is widely used in scientometrics.…”

Section: Local Computation Of Core Numbersmentioning

confidence: 99%

The core decomposition of networks: theory, algorithms and applications

et al. 2019

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The core decomposition of networks has attracted significant attention due to its numerous applications in real-life problems. Simply stated, the core decomposition of a network (graph) assigns to each graph node v, an integer number c(v) (the core number), capturing how well v is connected with respect to its neighbors. This concept is strongly related to the concept of graph degeneracy, which has a long history in Graph Theory. Although the core decomposition concept is extremely simple, there is an enormous interest in the topic from diverse application domains, mainly because it can be used to analyze a network in a simple and concise manner by quantifying the significance of graph nodes. Therefore, there exists a respectable number of research works that either propose efficient algorithmic techniques under different settings and graph types or apply the concept to another problem or scientific area. Based on this large interest in the topic, in this survey, we perform an in-depth discussion of core decomposition, focusing mainly on: i) the basic theory and fundamental concepts, ii) the algorithmic techniques proposed for computing it efficiently under different settings, and iii) the applications that can benefit significantly from it.

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“…This is because its parallelization would require parallel algorithms for computing graph degeneracy ordering (Line 3 of Algorithm 5) and for graph coloring (Line 6 of Algorithm 5), whose studies are beyond the scope of this paper. Specifically, designing practical algorithms for the former (i.e., parallel graph degeneracy ordering) has been preliminarily investigated in [20,44,52], but no practical algorithm with good solution quality for the latter (i.e., parallel graph coloring) is known. Note that the existing algorithms for parallel graph coloring typically use O(Δ) colors for a graph with maximum vertex degree Δ [19,41], which is ineffective for the coloring-based upper bound (this would make it degenerate to the degree-based upper bound).…”

Section: Parallelize Our Algorithmsmentioning

confidence: 99%

Efficient maximum clique computation and enumeration over large sparse graphs

Chang

2020

The VLDB Journal

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This paper studies the problem of maximum clique computation (MCC) over sparse graphs, as large real-world graphs are usually sparse. In the literature, the problem of MCC over sparse graphs has been studied separately and less extensively than its dense counterpart-MCC over dense graphs-and advanced algorithmic techniques that are developed for MCC over dense graphs have not been utilized in the existing MCC solvers for sparse graphs. In this paper, we design an algorithm MC-BRB for sparse graphs which transforms an instance of MCC over a large sparse graph G to instances of k-clique finding (KCF) over dense subgraphs of G, each of which can be computed by the existing MCC solvers for dense graphs. To further improve the efficiency, we then develop a new branch-reduce-&-bound framework for KCF over dense graphs by proposing light-weight reducing techniques and leveraging the advanced branching and bounding techniques that are used in the existing MCC solvers for dense graphs. In addition, we also design an ego-centric algorithm MC-EGO for heuristically computing a near-maximum clique in near-linear time, and we extend our MC-BRB algorithm to enumerate all maximum cliques. Finally, we parallelize our algorithms to exploit multiple CPU cores. We conduct extensive empirical studies on large real graphs and demonstrate the efficiency and effectiveness of our techniques. KeywordsMaximum clique computation • Maximum clique enumeration • Large sparse graph • Branch-bound-and-reduce • Reducing techniques Footnote 1 continued |V | 2 ) memory consumption is still inevitable; note that the state-of-theart MCC-Dense solver MoMC [34] also materializes the complement graph of the input graph, i.e., explicitly stores the non-neighbors of each vertex, for efficient processing.

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Local algorithms for hierarchical dense subgraph discovery

Cited by 61 publications

References 45 publications

Parallel Clique Counting and Peeling Algorithms

Parallel Clique Counting and Peeling Algorithms

The core decomposition of networks: theory, algorithms and applications

Efficient maximum clique computation and enumeration over large sparse graphs

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