A NUMA-Aware Parallel Truss Decomposition Algorithm for Large Scale Graphs

Truss decomposition algorithm is to decompose a graph into a hierarchical subgraph structure. A k-truss (k >= 2) is a subgraph that each edge is in at least k - 2 triangles. The existing algorithm is to first compute the number of triangles for each edge, and then iteratively increase k to peel off the edges that are not in the (k + 1)-truss. Due to the scale of the data and the intensity of computations, truss decomposition algorithm on the billion-side graph may take more than hours on a commodity server. In addition, today, more servers adopt NUMA architecture, which also affects the scalability of the algorithm. Therefore, we propose a NUMA-aware shared-memory parallel algorithm to accelerate the truss decomposition for NUMA systems by (1) computing different levels of k-truss between each NUMA nodes (2) dividing the range of k heuristically to ensure load balance (3) optimizing data structure and triangle counting method to reduce remote memory access, data contention and data skew. Our experiments show that on real-world datasets our OpenMP implementation can accelerate truss decomposition effectively on NUMA systems.