This repository contains code for our SPAA paper "Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable" (SPAA'18). It includes implementations of the following parallel graph algorithms:

Clustering Problems

• SCAN Graph Clustering
• Graph-Based Hierarchical Agglomerative Clustering (Graph HAC)

Connectivity Problems

• Low-Diameter Decomposition
• Connectivity
• Spanning Forest
• Biconnectivity
• Minimum Spanning Tree
• Strongly Connected Components

Covering Problems

• Coloring
• Maximal Matching
• Maximal Independent Set
• Approximate Set Cover

Eigenvector Problems

• PageRank

Substructure Problems

• Triangle Counting
• Approximate Densest Subgraph
• k-Core (Coreness)
• Degeneracy Ordering (Low-Outdegree Orientation)
• k-Clique Counting
• 5-Cycle Counting
• k-Truss

Shortest Path Problems

• Unweighted SSSP (Breadth-First Search)
• General Weight SSSP (Bellman-Ford)
• Integer Weight SSSP (Weighted Breadth-First Search)
• Single-Source Betweenness Centrality
• Single-Source Widest Path
• k-Spanner

The code for these applications is located in the benchmark directory. The implementations are based on the Ligra/Ligra /Julienne graph processing frameworks. The framework code is located in the src directory.

If you use our work, please cite our paper:

@inproceedings{dhulipala2018theoretically,
  author    = {Laxman Dhulipala and
               Guy E. Blelloch and
               Julian Shun},
  title     = {Theoretically Efficient Parallel Graph Algorithms Can Be Fast and
               Scalable},
  booktitle = {ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)},
  year      = {2018},
}

Compiler:

• g >= 7.4.0 with support for Cilk Plus
• g >= 7.4.0 with pthread support (Homemade Scheduler)

Build system:

• Bazel 2.1.0
• Make --- though our primary build system is Bazel, we also maintain Makefiles for those who wish to run benchmarks without installing Bazel.

The default compilation uses a lightweight scheduler developed at CMU (Homemade) for parallelism, which results in comparable performance to Cilk Plus. The half-lengths for certain functions such as histogramming are lower using Homemade, which results in better performance for codes like KCore.

The benchmark supports both uncompressed and compressed graphs. The uncompressed format is identical to the uncompressed format in Ligra. The compressed format, called bytepd_amortized (bytepda) is similar to the parallelByte format used in Ligra , with some additional functionality to support efficiently packs, filters, and other operations over neighbor lists.

To compile codes for graphs with more than 2^32 edges, the GBBSLONG command-line parameter should be set. If the graph has more than 2^32 vertices, the GBBSEDGELONG command-line parameter should be set. Note that the codes have not been tested with more than 2^32 vertices, so if any issues arise please contact Laxman Dhulipala.

To compile with the Cilk Plus scheduler instead of the Homegrown scheduler, use the Bazel configuration --config=cilk. To compile using OpenMP instead, use the Bazel configuration --config=openmp. To compile serially instead, use the Bazel configuration --config=serial. (For the Makefiles, instead set the environment variables CILK, OPENMP, or SERIAL respectively.)

To build:

# Load external libraries as submodules. (This only needs to be run once.)
git submodule update --init

# For Bazel:
$ bazel build  //...  # compiles all benchmarks

# For Make:
# First set the appropriate environment variables, e.g., first run
# `export CILK=1` to compile with Cilk Plus.
# After that, build using `make`.
$ cd benchmarks/BFS/NonDeterministicBFS  # go to a benchmark
$ make

Note that the default compilation mode in bazel is to build optimized binaries (stripped of debug symbols). You can compile debug binaries by supplying -c dbg to the bazel build command.

The following commands cleans the directory:

# For Bazel:
$ bazel clean  # removes all executables

# For Make:
$ make clean  # removes executables for the current directory

The applications take the input graph as input as well as an optional flag "-s" to indicate a symmetric graph. Symmetric graphs should be called with the "-s" flag for better performance. For example:

# For Bazel:
$ bazel run //benchmarks/BFS/NonDeterministicBFS:BFS_main -- -s -src 10 ~/gbbs/inputs/rMatGraph_J_5_100
$ bazel run //benchmarks/IntegralWeightSSSP/JulienneDBS17:wBFS_main -- -s -w -src 15 ~/gbbs/inputs/rMatGraph_WJ_5_100

# For Make:
$ ./BFS -s -src 10 ../../../inputs/rMatGraph_J_5_100
$ ./wBFS -s -w -src 15 ../../../inputs/rMatGraph_WJ_5_100

Note that the codes that compute single-source shortest paths (or centrality) take an extra -src flag. The benchmark is run four times by default, and can be changed by passing the -rounds flag followed by an integer indicating the number of runs.

On NUMA machines, adding the command "numactl -i all " when running the program may improve performance for large graphs. For example:

$ numactl -i all bazel run [...]

We make use of the bytePDA format in our benchmark, which is similar to the parallelByte format of Ligra , extended with additional functionality. We have provided a converter utility which takes as input an uncompressed graph and outputs a bytePDA graph. The converter can be used as follows:

# For Bazel:
bazel run //utils:compressor -- -s -o ~/gbbs/inputs/rMatGraph_J_5_100.bytepda ~/gbbs/inputs/rMatGraph_J_5_100
bazel run //utils:compressor -- -s -w -o ~/gbbs/inputs/rMatGraph_WJ_5_100.bytepda ~/gbbs/inputs/rMatGraph_WJ_5_100

# For Make:
./compressor -s -o ../inputs/rMatGraph_J_5_100.bytepda ../inputs/rMatGraph_J_5_100
./compressor -s -w -o ../inputs/rMatGraph_WJ_5_100.bytepda ../inputs/rMatGraph_WJ_5_100

After an uncompressed graph has been converted to the bytepda format, applications can be run on it by passing in the usual command-line flags, with an additional -c flag.

# For Bazel:
$ bazel run //benchmarks/BFS/NonDeterministicBFS:BFS_main -- -s -c -src 10 ~/gbbs/inputs/rMatGraph_J_5_100.bytepda

# For Make:
$ ./BFS -s -c -src 10 ../../../inputs/rMatGraph_J_5_100.bytepda
$ ./wBFS -s -w -c -src 15 ../../../inputs/rMatGraph_WJ_5_100.bytepda

When processing large compressed graphs, using the -m command-line flag can help if the file is already in the page cache, since the compressed graph data can be mmap'd. Application performance will be affected if the file is not already in the page-cache. We have found that using -m when the compressed graph is backed by SSD results in a slow first-run, followed by fast subsequent runs.

We make use of a binary-graph format in our benchmark. The binary representation stores the representation we use for in-memory processing (compressed sparse row) directly on disk, which enables applications to avoid string-conversion overheads associated with the adjacency graph format described below. We have provided a converter utility which takes as input an uncompressed graph (e.g., in adjacency graph format) and outputs this graph in the binary format. The converter can be used as follows:

# For Bazel:
bazel run //utils:compressor -- -s -o ~/gbbs/inputs/rMatGraph_J_5_100.binary ~/gbbs/inputs/rMatGraph_J_5_100

# For Make:
./compressor -s -o ../inputs/rMatGraph_J_5_100.binary ../inputs/rMatGraph_J_5_100

After an uncompressed graph has been converted to the binary format, applications can be run on it by passing in the usual command-line flags, with an additional -b flag. Note that the application will always load the binary file using mmap.

# For Bazel:
$ bazel run //benchmarks/BFS/NonDeterministicBFS:BFS_main -- -s -b -src 10 ~/gbbs/inputs/rMatGraph_J_5_100.binary

# For Make:
$ ./BFS -s -b -src 10 ../../../inputs/rMatGraph_J_5_100.binary

Note that application performance will be affected if the file is not already in the page-cache. We have found that using -m when the binary graph is backed by SSD or disk results in a slow first-run, followed by fast subsequent runs.

We support the adjacency graph format used by the Problem Based Benchmark suite and Ligra.

The adjacency graph format starts with a sequence of offsets one for each vertex, followed by a sequence of directed edges ordered by their source vertex. The offset for a vertex i refers to the location of the start of a contiguous block of out edges for vertex i in the sequence of edges. The block continues until the offset of the next vertex, or the end if i is the last vertex. All vertices and offsets are 0 based and represented in decimal. The specific format is as follows:

AdjacencyGraph
<n>
<m>
<o0>
<o1>
...
<o(n-1)>
<e0>
<e1>
...
<e(m-1)>

This file is represented as plain text.

Weighted graphs are represented in the weighted adjacency graph format. The file should start with the string "WeightedAdjacencyGraph". The m edge weights should be stored after all of the edge targets in the .adj file.

Using SNAP graphs

Graphs from the SNAP dataset collection are commonly used for graph algorithm benchmarks. We provide a tool that converts the most common SNAP graph format to the adjacency graph format that GBBS accepts. Usage example:

# Download a graph from the SNAP collection.
wget https://snap.stanford.edu/data/wiki-Vote.txt.gz
gzip --decompress ${PWD}/wiki-Vote.txt.gz
# Run the SNAP-to-adjacency-graph converter.
# Run with Bazel:
bazel run //utils:snap_converter -- -s -i ${PWD}/wiki-Vote.txt -o <output file>
# Or run with Make:
#   cd utils
#   make snap_converter
#   ./snap_converter -s -i <input file> -o <output file>