Parallelizing approximate single-source personalized PageRank queries on shared memory

Abstract

Given a directed graph G, a source node s, and a target node t, the personalized PageRank (PPR) $\pi (s,t)$ measures the importance of node t with respect to node s. In this work, we study the single-source PPR query, which takes a source node s as input and outputs the PPR values of all nodes in G with respect to s. The single-source PPR query finds many important applications, e.g., community detection and recommendation. Deriving the exact answers for single-source PPR queries is prohibitive, so most existing work focuses on approximate solutions. Nevertheless, existing approximate solutions are still inefficient, and it is challenging to compute single-source PPR queries efficiently for online applications. This motivates us to devise efficient parallel algorithms running on shared-memory multi-core systems. In this work, we present how to efficiently parallelize the state-of-the-art index-based solution FORA, and theoretically analyze the complexity of the parallel algorithms. Theoretically, we prove that our proposed algorithm achieves a time complexity of $O(W/P+\log ^2{n})$, where W is the time complexity of sequential FORA algorithm, P is the number of processors used, and n is the number of nodes in the graph. FORA includes a forward push phase and a random walk phase, and we present optimization techniques to both phases, including effective maintenance of active nodes, improving the efficiency of memory access, and cache-aware scheduling. Extensive experimental evaluation demonstrates that our solution achieves up to 37$\times$ speedup on 40 cores and 3.3$\times$ faster than alternatives on 40 cores. Moreover, the forward push alone can be used for local graph clustering, and our parallel algorithm for forward push is 4.8$\times$ faster than existing parallel alternatives.