PageRank

Problem Specification

Input

$G=(V, E)$, an undirected graph.

Output

$\mathcal{P}$, a mapping from each vertex to its PageRank value after a single iteration of PageRank.

Algorithm Implementations

Our PageRank algorithm terminates once the $l_{1}$ norm of the differences between PageRank values between iterations is below $\epsilon$. The algorithm that we implement is an extension of the implementation of PageRank described in Ligra. More details about our implementation can be found in Section 6.5 of [1].

The code for our implemenation is available here.

Cost Bounds

The algorithm runs in $O(n + m)$ work and $O(\log n)$ depth for a single iteration of PageRank.

Compiling and Running

The benchmark can be compiled by running:

bazel build -c opt //benchmarks/PageRank/...

It can then be run on a test input graph in the uncompressed format as follows:

numactl -i all ./bazel-bin/benchmarks/PageRank/PageRank_main -s -m -src 1 inputs/rMatGraph_J_5_100

It can then be run on a test input graph in the compressed format as follows:

numactl -i all ./bazel-bin/benchmarks/PageRank/PageRank_main -s -c -m -src 1 inputs/rMatGraph_J_5_100.bytepda

References

[1] Laxman Dhulipala, Guy Blelloch, and Julian Shun
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 393-404, 2018.