Positive-Weight SSSP (Delta Stepping)

Problem Specification

Input

$G=(V, E, w)$, a weighted graph with positive edge weights, and a source, $s \in V$. The input graph can either be undirected, or directed.

Output

Output: $D$, a mapping where $D[v]$ is the shortest path distance from $s$ to $v$ in $G$ and $\infty$ if $v$ is unreachable.

Algorithm Implementations

The code for our implemenation is available here. Our GBBS implementation is from the Julienne paper [1].

Cost Bounds

Please [1] for details.

Compiling and Running

The benchmark can be compiled by running:

bazel build -c opt //benchmarks/PositiveWeightSSSP/DeltaStepping:DeltaStepping

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

numactl -i all ./bazel-bin/benchmarks/PositiveWeightSSSP/DeltaStepping/DeltaStepping_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/PositiveWeightSSSP/DeltaStepping/DeltaStepping_main -s -c -m -src 1 inputs/rMatGraph_J_5_100.bytepda

References

[1] Laxman Dhulipala, Guy Blelloch, and Julian Shun
Julienne: A Framework for Parallel Graph Algorithms using Work-efficient Bucketing
Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 293-304, 2017.

[2] 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.