The shortest path is not always a straight line: leveraging semi-metricity in graph analysis

In this paper, we leverage the concept of the metric backbone to improve the efficiency of large-scale graph analytics. The metric backbone is the minimum subgraph that preserves the shortest paths of a weighted graph. We use the metric backbone in place of the original graph to compute various graph metrics exactly or with good approximation. By computing on a smaller graph, we improve the performance of graph analytics applications on two different systems, a batch graph processing system and a graph database. Further, we provide an algorithm for the computation of the metric backbone on large graphs. While one can compute the metric backbone by solving the all-pairs-shortest-paths problem, this approach incurs prohibitive time and space complexity for big graphs. Instead, we propose a heuristic that makes computing the metric backbone practical even for large graphs. Additionally, we analyze several real datasets of different sizes and domains and we show that we can approximate the metric backbone by removing only first-order semi-metric edges; edges for which a shorter two-hop path exists. We provide a distributed implementation of our algorithm and apply it in large scale scenarios. We evaluate our algorithm using a variety of real graphs, including a Facebook social network subgraph of ~50 billion edges. We measure the impact of using the metric backbone on runtime performance in two graph management systems. We achieve query speedups of up to 6.7x in the Neo4j commercial graph database and job speedups of up to 6x in the Giraph graph processing system.