Locality-based Graph Reordering for Processing Speed-Ups and Impact of Diameter

💡 Research Summary

The paper addresses the dominant performance bottleneck in graph analytics—cache misses caused by irregular memory accesses. While prior work has focused on improving cache replacement policies or prefetching, this study investigates graph reordering as a means to enhance both temporal and spatial locality. The authors propose a lightweight reordering scheme called LOrder that simultaneously leverages two intrinsic properties of natural graphs: the power‑law degree distribution (a small set of “hot” high‑degree vertices) and the presence of community structures (clusters of densely connected vertices).

The problem is formally defined as finding a permutation φ that assigns new vertex IDs to minimize total cache misses during typical graph algorithms, while also keeping the reordering overhead low and preserving the original graph’s structural locality. Existing reordering methods are critiqued: GOrder maximizes a score based on common neighbors and direct adjacency but incurs high greedy‑algorithm overhead; S‑Order introduces hyper‑nodes to group cold vertices but does not effectively co‑locate hot vertices; N‑Order sorts vertices by hotness and then performs a BFS‑style traversal, doubling traversal cost; DBG groups vertices by degree within fixed partitions, ignoring actual adjacency.

LOrder’s core idea is to first split all vertices into “hot” (degree > average) and “cold” groups. Within each group, vertices are further partitioned into disjoint but complete “localities” that correspond to communities. Two implementations are explored: (1) a seed‑based version where the unvisited vertex with the smallest original index becomes the seed of a community, and (2) a ground‑truth version where each connected component of the original graph is treated as a community. Within each locality, the vertex order follows a BFS traversal, preserving the original neighbor relationships. Hot vertices are placed before cold ones, ensuring that cache lines tend to contain many high‑reuse vertices (improving temporal locality) while the BFS‑based ordering retains spatial locality of neighborhoods.

The experimental evaluation uses five representative graph algorithms—Breadth‑First Search (BFS), Connected Components (CC), CCSV (a custom traversal), PageRank (PR), and Betweenness Centrality (BC)—on several real‑world datasets (social networks, web graphs, geographic networks). LOrder is compared against the original graph (no reordering) and four state‑of‑the‑art reordering schemes (GOrder, S‑Order, N‑Order, DBG). Results show that LOrder achieves an average speed‑up of 1.2× over the best existing method and up to 7× on graphs with large diameters, particularly benefiting BFS and CC where neighborhood‑based access patterns dominate. The ground‑truth version incurs higher reordering time but yields lower post‑reordering execution times, making it advantageous when the reordered graph will be reused across many analyses. The authors also investigate the impact of graph diameter: larger diameters amplify the benefits of locality‑preserving reordering because the average distance between vertices after reordering shrinks more dramatically, leading to tighter memory access patterns and fewer cache evictions.

In conclusion, LOrder demonstrates that a modest‑cost reordering that respects both hot‑vertex clustering and community structure can substantially reduce cache misses without sacrificing spatial locality. The dual‑version design offers flexibility: a fast seed‑based approach for one‑off analyses and a more thorough component‑based approach for repeated workloads. Future work is suggested in the areas of dynamic graph reordering, hardware‑aware cache policy integration, and automated diameter‑aware parameter tuning.