Explicit Ordering Refinement for Accelerating Irregular Graph Analysis

Abstract

Vertex reordering for efficient memory access in extreme-scale graph-based data analysis shows considerable improvement to the cache efficiency and runtimes of widely used graph analysis algorithms. Despite this, modern efficient ordering methods are often heuristic-based and do not directly optimize some given metrics. Thus, this paper conducts an experimental study into explicit metric-based vertex ordering optimization. We introduce a universal graph partitioning-inspired approach focusing on CPU shared-memory parallelism to the vertex ordering problem through the explicit refinement of low-degree vertices using the Linear Gap Arrangement and Log Gap Arrangement problems as comprehensive metrics for ordering improvement. This degree-based refinement method is evaluated upon a number of initial orderings with timing and cache efficiency results relative to three shared-memory graph analytic algorithms: PageRank, Louvain and the Multistep algorithm. Applying refinement, we observe runtime improvements of up to 15x on the ClueWeb09 graph and up to 4x improvements to cache efficiency on a variety of network types and initial orderings, demonstrating the feasibility of an optimization approach to the vertex ordering problem at a large scale.