Modeling the Locality in Graph Traversals

An increasing number of applications in physical and social sciences require the analysis of large graphs. The efficiency of these programs strongly depends on their memory usage especially the locality of graph data access. Intuitively, the locality in computation should reflect the locality in graph topology. Existing locality models, however, operate either at program level for regular loops and arrays or at trace level for arbitrary access streams. They are not sufficient to characterize the relation between locality and connectivity. This paper presents a new metrics called the vertex distance and uses it to model the locality in breadth-first graph traversal (BFS). It shows three models that use the average node degree and the edge distribution to predict the number of BFS levels and the reuse distance distribution of BFS. Finally, it evaluates the new models using random and non-random graphs.