A round-efficient distributed betweenness centrality algorithm

Hoang, Loc; Pontecorvi, Matteo; Dathathri, Roshan; Gill, Gurbinder; You, Bozhi; Pingali, Keshav; Ramachandran, Vijaya

doi:10.1145/3293883.3295729

Cited by 33 publications

(23 citation statements)

References 51 publications

(94 reference statements)

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“…It should also be interesting to see how our algorithm performs in real systems (such as D-Galois [HPD+19]), and to see if our ideas are useful in computing various centrality measures (e.g. [HPD+19]).…”

Section: Open Problemsmentioning

confidence: 99%

Distributed exact weighted all-pairs shortest paths in near-linear time

Bernstein

Nanongkai

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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In the distributed all-pairs shortest paths problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds (typically called time complexity). The problem admits (1 + o( 1))-approximation Θ(n)-time algorithm and a nearly-tight Ω(n) lower bound [Nanongkai, STOC'14; Lenzen and Patt-Shamir PODC'15] 1 . For the exact case, Elkin [STOC'17] presented an O(n 5/3 log 2/3 n) time bound, which was later improved to Õ(n 5/4 ) [Huang, Nanongkai, Saranurak FOCS'17]. It was shown that any super-linear lower bound (in n) requires a new technique [Censor-Hillel, Khoury, Paz, DISC'17], but otherwise it remained widely open whether there exists a Õ(n)-time algorithm for the exact case, which would match the best possible approximation algorithm.This paper resolves this question positively: we present a randomized (Las Vegas) Õ(n)-time algorithm, matching the lower bound up to polylogarithmic factors. Like the previous Õ(n 5/4 ) bound, our result works for directed graphs with zero (and even negative) edge weights. In addition to the improved running time, our algorithm works in a more general setting than that required by the previous Õ(n 5/4 ) bound; in our setting (i) the communication is only along edge directions (as opposed to bidirectional), and (ii) edge weights are arbitrary (as opposed to integers in {1, 2, . . . , poly(n)}). The previously best algorithm for this more difficult setting required Õ(n 3/2 ) time [Agarwal and Ramachandran, ArXiv'18] (this can be improved to Õ(n 4/3 ) if one allows bidirectional communication).Our algorithm is extremely simple and relies on a new technique called Random Filtered Broadcast. Given any sets of nodes A, B ⊆ V and assuming that every b ∈ B knows all distances from nodes in A, and every node v ∈ V knows all distances from nodes in B, we want every v ∈ V to know DistThrough B (a, v) = min b∈B dist(a, b) + dist(b, v) for every a ∈ A. Previous works typically solve this problem by broadcasting all knowledge of every b ∈ B, causing super-linear edge congestion and time. We show a randomized algorithm that can reduce edge congestions and thus solve this problem in Õ(n) expected time.1 Θ, Õ and Ω hide polylogarithmic factors. Note that the lower bounds also hold even in the unweighted case and in the weighted case with polynomial approximation ratios [LP13, HW12, PRT12, Nan14].

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Section: Open Problemsmentioning

confidence: 99%

Distributed exact weighted all-pairs shortest paths in near-linear time

Bernstein

Nanongkai

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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“…The first approach is to adapt the betweenness centrality algorithm for distributed computation. Recently, many algorithms [21,25,39] have been proposed, which extend the computation from a single machine to a cluster of high performance machines. This approach reduces the computation time significantly for large graphs.…”

Section: Betweenness Centralitymentioning

confidence: 99%

Graph Neural Networks for Fast Node Ranking Approximation

Maurya

Liu²,

Murata

2021

ACM Trans. Knowl. Discov. Data

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Graphs arise naturally in numerous situations, including social graphs, transportation graphs, web graphs, protein graphs, etc. One of the important problems in these settings is to identify which nodes are important in the graph and how they affect the graph structure as a whole. Betweenness centrality and closeness centrality are two commonly used node ranking measures to find out influential nodes in the graphs in terms of information spread and connectivity. Both of these are considered as shortest path based measures as the calculations require the assumption that the information flows between the nodes via the shortest paths. However, exact calculations of these centrality measures are computationally expensive and prohibitive, especially for large graphs. Although researchers have proposed approximation methods, they are either less efficient or suboptimal or both. We propose the first graph neural network (GNN) based model to approximate betweenness and closeness centrality. In GNN, each node aggregates features of the nodes in multihop neighborhood. We use this feature aggregation scheme to model paths and learn how many nodes are reachable to a specific node. We demonstrate that our approach significantly outperforms current techniques while taking less amount of time through extensive experiments on a series of synthetic and real-world datasets. A benefit of our approach is that the model is inductive, which means it can be trained on one set of graphs and evaluated on another set of graphs with varying structures. Thus, the model is useful for both static graphs and dynamic graphs. Source code is available at https://github.com/sunilkmaurya/GNN_Ranking

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“…Unwanted network failures can cause loss of significant amount for voice and data traffic [15]. Especially when new technologies are being developed, new concerns were also raised [16].…”

Section: Related Workmentioning

confidence: 99%

Robustness metrics for optical networks

Zainiar

Iqbal

Supa’at

et al. 2020

IJEECS

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Telecommunication networks are vulnerable towards single or simultaneous nodes/links failures, which may lead to the disruption of network areas. The failures may cause performance degradation, reduced quality of services, reduced nodes/links survivability, stability, and reliability. Therefore, it is important to measure and enhance the network robustness, via the use of robustness metrics. This paper gives an overview of several robustness metrics that are commonly used for optical networks, from the structural, centrality and functional perspectives.

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A round-efficient distributed betweenness centrality algorithm

Cited by 33 publications

References 51 publications

Distributed exact weighted all-pairs shortest paths in near-linear time

Distributed exact weighted all-pairs shortest paths in near-linear time

Graph Neural Networks for Fast Node Ranking Approximation

Robustness metrics for optical networks

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