Replaced Vector data structure by BitSet in greedy_color

[AntoineBut]

This PR adresses #378 .

Replacing Vector with a Set yields immediate speedup of 50-100x on my machine.

As the we are using dense sets of integers from 1 to the number of colors to color the graph (i.e relatively small integers), BitSet implementation seems to be the most appropriate here. (and is also faster on my machine, even though I have not tested on an extensive benchmark suite)

Im open to feedback of course (I am still pretty new here) :))

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.31%. Comparing base (615afe4) to head (0104925).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #379   +/-   ##
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  Coverage   97.31%   97.31%           
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  Files         120      120           
  Lines        6953     6954    +1     
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+ Hits         6766     6767    +1     
  Misses        187      187           

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[gdalle]

Thanks a lot for the contribution!

[gdalle]

@AntoineBut can you check what my change from BitSet to Set does in terms of performance?
It might be faster in theory but slower in practice, at least on instances of moderate size.

[AntoineBut]

@gdalle Here are results from a rapid benchmarking :

Setup :
3 types of synthetic graphs, all in 3 sizes :
1 graph imported from Snap

julia> doro_small = dorogovtsev_mendes(10)
{10, 17} undirected simple Int64 graph

julia> doro_med = dorogovtsev_mendes(300)
{300, 597} undirected simple Int64 graph

julia> doro_large = dorogovtsev_mendes(100_000)
{100000, 199997} undirected simple Int64 graph

julia> bara_small = barabasi_albert(10, 2)
{10, 16} undirected simple Int64 graph

julia> bara_med = barabasi_albert(300, 2)
{300, 596} undirected simple Int64 graph

julia> bara_large = barabasi_albert(100_000, 2)
{100000, 199996} undirected simple Int64 graph

julia> complete_small = complete_graph(10)
{10, 45} undirected simple Int64 graph

julia> complete_med = complete_graph(300)
{300, 44850} undirected simple Int64 graph

julia> complete_large = complete_graph(10_000)
{10000, 49995000} undirected simple Int64 graph

# Real-world data graph 
julia> twitch_graph = loadgraph("/Users/antoine/Documents/GitHub/ParallelGraphs.jl/benchmark/data/large_twitch_edges.csv", "twitch", EdgeListFormat())
{168116, 6797558} directed simple Int64 graph

Results :

	Set{T}	BitSet
Barabasi Albert
Small	662.556 ns (9 allocations: 928 bytes)	411.692 ns (6 allocations: 624 bytes)
Med	13.791 μs (10 allocations: 11.28 KiB)	7.208 μs (7 allocations: 10.98 KiB)
Large	7.714 ms (15 allocations: 3.15 MiB)	4.736 ms (12 allocations: 3.15 MiB)
Dorogostev Mendes
Small	638.643 ns (9 allocations: 928 bytes)	404.084 ns (6 allocations: 624 bytes)
Med	13.958 μs (10 allocations: 11.28 KiB)	7.229 μs (7 allocations: 10.98 KiB)
Large	7.721 ms (15 allocations: 3.15 MiB)	4.740 ms (12 allocations: 3.15 MiB)
Complete Graph
Small	827.465 ns (9 allocations: 928 bytes)	479.492 ns (6 allocations: 624 bytes)
Med	378.917 μs (18 allocations: 21.38 KiB)	128.459 μs (7 allocations: 8.44 KiB)
Large	457.570 ms (30 allocations: 438.27 KiB)	123.255 ms (12 allocations: 246.50 KiB)
Twitch Graph
	46.081 ms (18 allocations: 5.29 MiB)	31.722 ms (12 allocations: 5.29 MiB)

I tried to represent graphs that behave differently with respect to coloring, some of them are colored with only 5 colors (even on thousands of vertices) and the complete graph is colored in N colors.
BitSet was faster in all configurations I tried, with speedup ranging from x1,4 to x3,5.

I hope that adresses your concerns!
Let me know if there is anything else :)

[gdalle]

Just out of curiosity, could you try with a BitVector? Then we'll pick the best and merge. My gut tells me it may be as fast as BitSet sometimes