A Simple Yet Effective Balanced Edge Partition Model for Parallel Computing

Abstract

Graph edge partition models have recently become an appealing alternative to graph vertex partition models for distributed computing due to their flexibility in balancing loads and their performance in reducing communication cost [6, 16]. In this paper, we propose a simple yet effective graph edge partitioning algorithm. In practice, our algorithm provides good partition quality (and better than similar state-of-the-art edge partition approaches, at least for power-law graphs) while maintaining low partition overhead. In theory, previous work [6] showed that an approximation guarantee of O ( d max √ log n log k ) apply to the graphs with m =Ω( k 2 ) edges ( k is the number of partitions). We further rigorously proved that this approximation guarantee hold for all graphs. We show how our edge partition model can be applied to parallel computing. We draw our example from GPU program locality enhancement and demonstrate that the graph edge partition model does not only apply to distributed computing with many computer nodes, but also to parallel computing in a single computer node with a many-core processor.

Fast load balance parallel graph analytics with an automatic graph data structure selection algorithm

“…Previously studied vertex reordering algorithms are computationally more complex. The algorithm presented by Li et al [13] has polynomial time complexity in |V |. Gorder [14] takes…”

“…Gonzalez et al proposed vertex cut, a parallel streaming partitioning algorithm that minimizes vertex replication [6]. Li et al [13] and Bourse et al [12] proposed efficient edge-balanced partitioning methods. Bourse et al [12] moreover investigate the interplay between edge balance and vertex balance, which is non-trivial if edge cuts are simultaneously minimized.…”

“…We demonstrate that ordering of GraphGrind has low time complexity and can complete in O(n log P ) steps for n vertices and P partitions. In contrast, many graph partitioning algorithms have been proposed [11], [12], [13], [14], [15] with significantly higher time complexity.…”

TopoX

“…However, the super-vertex degrees will not be known until all fusion operations complete, causing time-consuming fissionafter-fusion dependencies. Inspired by the splitting process on high-degree vertices in previous studies [15,10,30,39], we perform fission without waiting for fusion by (i) splitting a high-degree vertex (v h ) into n sub-vertices (where n is the number of workers) each being assigned to one worker, and (ii) assigning v h 's edges (e = <u, v h > or <v h , u>) according to (the hash of) the opposite ends (vertices u).…”

“…TopoX differs from them in adopting a novel refactorization scheme to achieve a balanced graph before partitioning by leveraging the topology information. Recently proposed vertex-splitting methods [30,39] split a high-degree vertex into small ones to avoid bottlenecks, but they cannot place a large set of neighboring vertices in one machine. TopoX outperforms these systems in computation while only introducing small overhead.…”