A faster parallel algorithm and efficient multithreaded implementations for evaluating betweenness centrality on massive datasets

Madduri, Kamesh; Ediger, David; Jiang, Karl; Bader, David A.; Chavarŕıa-Miranda, Daniel

doi:10.1109/ipdps.2009.5161100

Cited by 102 publications

(62 citation statements)

References 12 publications

(14 reference statements)

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“…Approximation algorithms and parallel algorithms for BC have been considered in [2,7], [16] respectively. Lee et al [14] present a framework called QUBE (Quick Update of BEtweenness centrality) which allows edges to be inserted and deleted from the graph, and recently, Singh et al [23] build on the work of Lee et al [14] to allow nodes to be added and deleted.…”

Section: Related Workmentioning

confidence: 99%

Betweenness Centrality – Incremental and Faster

Nasre

Pontecorvi

Ramachandran

2014

Mathematical Foundations of Computer Science 2014

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Abstract. We consider the incremental computation of the betweenness centrality (BC) of all vertices in a graph G = (V, E), directed or undirected, with positive real edge-weights. The current widely used algorithm is the Brandes algorithm that runs in O(mn + n 2 log n) time, where n = |V | and m = |E|. We present an incremental algorithm that updates the BC score of all vertices in G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(m n+n 2 ) time, where m is bounded by m * = |E * |, and E * is the set of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental update of a vertex v, where the edge update can be performed on any subset of edges incident to v. Our incremental algorithm is the first algorithm that is asymptotically faster on sparse graphs than recomputing with the Brandes algorithm even for a single edge update. It is also likely to be much faster than the Brandes algorithm on dense graphs since m * is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(scan(n 2 )+n·sort(m )) cache misses, where scan and sort are well-known measures for efficient caching. We also give a static BC algorithm that runs in time O(m * n + n 2 log n), which is faster than the Brandes algorithm on any graph with m = ω(n log n) and m * = o(m). IntroductionBetweenness centrality (BC) is a widely-used measure in the analysis of large complex networks. The BC of a node v in a network is the fraction of all shortest paths in the network that go through v, and this measure is often used as an index that determines the relative importance of v in the network. Some applications of BC include analyzing social interaction networks [12], identifying lethality in biological networks [21], and identifying key actors in terrorist networks [13,4]. Given the changing nature of the networks under consideration, it is desirable to have algorithms that compute BC faster than computing it from scratch after every change. Our main contribution is the first incremental algorithm for computing BC after an incremental update on an edge or on a vertex that is provably faster on sparse graphs than the widely used static algorithm by Brandes [3]. By an incremental update on an edge (u, v) we mean a decrease in the weight of an existing edge (u, v), or the addition of a new edge (u, v) with finite weight if (u, v) is not present in the graph; in an incremental vertex update, updates can occur on any subset of edges incident to v, including the addition of new edges.Let G = (V, E) be a graph with positive real edge weights. Let n = |V | and m = |E|. To state our result we need the following definitions. For a vertex x ∈ V , let m * x denote the number of edges that lie on shortest paths through x. Letm * denote the average over all m * x , i.e.,m * = 1 n x∈V m * x . Finally, let m * denote the total number of edges that lie on shortest paths in G. For our incr...

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Section: Related Workmentioning

confidence: 99%

Betweenness Centrality – Incremental and Faster

Nasre

Pontecorvi

Ramachandran

2014

Mathematical Foundations of Computer Science 2014

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“…• Second, although some parallel approaches for computing exact betweenness have been proposed [17,18,19,20,21], in general, it is still very costly for billion-node graphs. A straightforward parallel compuation of the exact betweenness has complexity Ω(|V | 2 ) [19], which is prohibitive on big graphs.…”

Section: Motivationmentioning

confidence: 99%

“…These approximate solutions do not consider parallelized optimization. Many versions of parallelized betweenness are also proposed [17,18,19,20,21] on different parallelized platforms, such as massive multithreaded computing platforms [17,18], distributed memory systems [19], and multi-core systems [20,21]. All these distributed betweenness algorithms only calculate exact betweenness, without considering how to devise an effective and approximate betweenness according to the characteristics of a corresponding distributed computing platform.…”

Section: Related Workmentioning

confidence: 99%

Toward a distance oracle for billion-node graphs

Shao

Wang

2013

Proc. VLDB Endow.

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The emergence of real life graphs with billions of nodes poses significant challenges for managing and querying these graphs. One of the fundamental queries submitted to graphs is the shortest distance query. Online BFS (breadth-first search) and offline pre-computing pairwise shortest distances are prohibitive in time or space complexity for billion-node graphs. In this paper, we study the feasibility of building distance oracles for billion-node graphs. A distance oracle provides approximate answers to shortest distance queries by using a pre-computed data structure for the graph. Sketch-based distance oracles are good candidates because they assign each vertex a sketch of bounded size, which means they have linear space complexity. However, state-of-the-art sketch-based distance oracles lack efficiency or accuracy when dealing with big graphs. In this paper, we address the scalability and accuracy issues by focusing on optimizing the three key factors that affect the performance of distance oracles: landmark selection, distributed BFS, and answer generation. We conduct extensive experiments on both real networks and synthetic networks to show that we can build distance oracles of affordable cost and efficiently answer shortest distance queries even for billion-node graphs.

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“…While this approach has been demonstrated to be highly effective in discovering community structure [25], the cost of computing centrality index and the need for recomputing after every step make the algorithm slow (Ω(n 3 ) even for sparse graphs with n vertices) and practical for only up to n ≈ 10 4 on single compute nodes. Nevertheless, there are shared memory parallel algorithms such as [22] for efficiently calculating betweenness centrality on graphs. A different approach [26] works on weighted graphs, where edge weights are distance measures, and uses Minimum Spanning Trees (MST) for clustering by taking advantage of the property that closely related groups tend to map to subtrees within an MST.…”

Section: Background and Related Workmentioning

confidence: 99%

An OpenMP algorithm and implementation for clustering biological graphs

Chapman

Kalyanaraman

2011

Proceedings of the 1st Workshop on Irregular Applications: Architectures and Algorithms

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Graph algorithms on parallel architectures present an interesting case study for irregular applications. Among the graph algorithms popular in scientific computing, graph clustering or community detection has numerous applications in computational biology. However, this operation also poses serious computational challenges because of irregular memory access patterns, large memory requirements, and their dependence on other auxiliary (also irregular) data structures to supplement processing. In this paper, we address the problem of graph clustering on shared memory machines. We present a new OpenMP-based parallel algorithm called pClust-sm, which uses adjacency lists, hash tables and unionfind data structures in parallel. The algorithm improves both the asymptotic runtime and memory complexities of a previous serial implementation. Preliminary results show that this algorithm can scale up to 8 threads (cores) of a shared memory machine on a real world metagenomics input graph with 1.2M vertices and 100M edges. More importantly, the new implementation drastically reduces the time to solution from the order of several hours to just over 4 minutes, and in addition, it enhances the problem size reach by at least one order of magnitude.

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A faster parallel algorithm and efficient multithreaded implementations for evaluating betweenness centrality on massive datasets

Cited by 102 publications

References 12 publications

Betweenness Centrality – Incremental and Faster

Betweenness Centrality – Incremental and Faster

Toward a distance oracle for billion-node graphs

An OpenMP algorithm and implementation for clustering biological graphs

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