Single-Source Shortest Path
Application Description
This benchmark computes the shortest path from a source node to all nodes in a directed graph with non-negative edge weights.
We have 2 distributed implementations of SSSP: a push-style and a pull-style. Both are bulk-synchronous parallel (BSP) implementations: execution proceeds in rounds, and synchronization of data among hosts occurs between rounds.
The push-style version checks a node to see if its distance has changed since the last round. If it has, it will update its neighbor's distances using its new distance and the weight of the edge that connects the two. The pull-style version goes over all nodes: all nodes check their in-neighbors, and if a neighbor has a distance that would result in a new shortest path distance once the edge is considered, then a node updates itself with its neighbors' data. Execution of both versions continues until there are no more nodes that are updated in a round.
Psuedocode for the computation step of the 2 implementations follows below:
| 1 2 3 4 5 6 7 | for (node n in graph) { if (n.distance != n.old_distance) { for (neighbor a of node n) { a.distance = min(n.distance + weight of edge(n,a), a.distance) } } } |
Figure 1: Pseudocode for SSSP Push computation
| 1 2 3 4 5 6 7 8 | for (node n in graph) { for (in-neighbor a of node n) { if (a.distance + weight of edge(a,n) < n.distance) { n.distance = a.distance + weight of edge(a,n) } } } } |
Figure 2: Pseudocode for SSSP Pull computation
Synchronization of the distance variable occurs between BSP rounds. A node will take the minimum distance value of all proxies that exist in the system for that node.
Performance
The graph below shows the strong scaling of sssp-push using both Bulk Synchronous Parallel (Gluon-Sync) and Bulk-Asynchronous Parallel (Gluon-Async) execution models which use a Gluon communication substrate. The experiments were conducted on Stampede Cluster (Stampede2), which is connected through Intel Omni-Path Architecture (peak bandwidth of 100Gbps). Each node has 2 Intel Xeon Platinum 8160 “Skylake” CPUs with 24 cores per CPU and 192GB DDR4 RAM. We use up to 128 CPU machines, each with 48 threads. We run on 4 graphs: clueweb12, uk14, wdc14, and wdc12. Most are real-world web-crawls: the web data commons hyperlink graph. wdc12, is the largest publicly available dataset. wdc14, clueweb12, and uk14 are all other large web-crawls.
