This repo implements following two papers using CUDA so as to accelerate MST computation:

1. Chapter 7 Fast Minimum Spanning Tree Computation of GPU Computing Gems, a data-parallel MST based on Boruvka's algorithm.
2. Fast and Memory-Efficient Minimum Spanning Tree on the GPU, a data-parallel Kruskal's MST algorithm, which lies between serial Kruskal's and parallel Boruvka's in terms of parallelism.

This is originally part of the benchmark suite. Thrust is heavily used.

The baselines are:

• serial Kruskal's algorithm with union find with weight and path-compression
• CPU multi-core parallel Kruskal's algorithm

The compare flows are gpuMST and gpuMSTdpk which are my implementations.

For data-parallel Boruvka's, result shows that on a GTX750ti & E1231v2 machine, on-par performance is achieved on random graphs, whereas better performances can be observed with sparse (grid) graph and power-law graphs.

And this approach is quite memory costly -- I cannot go beyond 2 million vertices with 10 million edges for random graph with my 2GB GPU memory.

1 : randLocalGraph_WE_5_2000000 :  -r 1 -o /tmp/ofile765486_563367 : '0.759'
1 : rMatGraph_WE_5_2000000 :  -r 1 -o /tmp/ofile138860_218538 : '0.655'
1 : 2Dgrid_WE_2000000 :  -r 1 -o /tmp/ofile8903_852545 : '0.159'
gpuMST : 0 : weighted time, min=0.524 median=0.524 mean=0.524

1 : randLocalGraph_WE_5_2000000 :  -r 1 -o /tmp/ofile399034_715347 : '0.65'
1 : rMatGraph_WE_5_2000000 :  -r 1 -o /tmp/ofile477678_439826 : '0.697'
1 : 2Dgrid_WE_2000000 :  -r 1 -o /tmp/ofile983504_141272 : '0.395'
serialMST : 0 : weighted time, min=0.58 median=0.58 mean=0.58

For data-parallel Kruskal's, result is much better -- it is more memory efficient and faster. With my 2GB GPU memory, I can push to 5 million vertices with 25 million edges (and maybe higher below 10 million vertices with 50 million edges, never tried...

Result shows that the performance is also better -- the speedup is more than 3x. In particular, as usual, for sparse 2d grid graph, the speedup is the best, while now the response to random graph is a little bit better than power-law, just as the pure serial one does.

In general, I think the performance gain mentioned in the paper is very similar to what I have observed, compared to either data-parallel Boruvka's or serial Kruskal's.

1 : randLocalGraph_WE_5_5000000 :  -r 1 -o /tmp/ofile609269_741536 : '0.604'
1 : rMatGraph_WE_5_5000000 :  -r 1 -o /tmp/ofile631862_452509 : '0.886'
1 : 2Dgrid_WE_5000000 :  -r 1 -o /tmp/ofile972092_45516 : '0.363'
gpuMSTdpk : 0 : weighted time, min=0.617 median=0.617 mean=0.617

1 : randLocalGraph_WE_5_5000000 :  -r 1 -o /tmp/ofile514914_278972 : '1.99'
1 : rMatGraph_WE_5_5000000 :  -r 1 -o /tmp/ofile295582_919992 : '2.54'
1 : 2Dgrid_WE_5000000 :  -r 1 -o /tmp/ofile576909_787203 : '1.19'
serialMST : 0 : weighted time, min=1.906 median=1.906 mean=1.906