Cloud Computing by Nick Antonopoulos & Lee Gillam

Author:Nick Antonopoulos & Lee Gillam
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

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We implement a more efficient version of BC introduced by Brandes [16]. For a graph with n vertices and m edges, this algorithm requires O(n+m) space. The algorithm runs in O(nm) and O(nm+n2log n) time on unweighted and weighted graphs, respectively [16]. Brandes algorithm traverses the vertices in nonincreasing order of their distance from source vertex (Brandes does not mandate use of a specific traversal algorithm for this purpose [16]). Once this is done, it backtracks through the frontiers to update sum of important values of each vertex [53]. However, it should be noted that in the case of AttributedGraph we use Dijkstra’s algorithm instead of BFS in order to account for edge weights. We do not do any approximation of BC, rather we calculate exact BC scores on large graphs.

In our BC algorithm at the beginning, Place 0 instantiates BetweennessCent- -rality class objects in all the places. After construction of each object, it invokes the method for constructing neighbor map that includes information of the neighbor connectivity. Once each object constructs their own neighbor map, each object runs Brandes on assigned vertices on them and calculates BC in parallel. Finally, betweenness scores are scattered among each place via a distributed all reduce operation, which are then reported as an array object from Place 0. A code snippet of our BC implementation on PlainGraph is shown in Fig. 7.4. Note that important X10 language constructs are highlighted in bold italics font in Figs. 7.4 and 7.5.

Fig. 7.4A code snippet of BC calculation on PlainGraph

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