Improve performance of bfs functions

[Tortar]

I added an optimization to these bfs functions which I benchmarked with

using Graphs, BenchmarkTools

gs = [path_graph(500),
      path_graph(5000),
      path_graph(50000),
      erdos_renyi(50, 0.5, seed=123),
      erdos_renyi(500, 0.5, seed=123),
      erdos_renyi(5000, 0.5, seed=123),
      complete_graph(50),
      complete_graph(500),
      complete_graph(5000)]

for g in gs
    n = nv(g)
    u = Int(n/5)
    dists = vec(fill(typemax(Int), (1, n)))
    t_1 = @belapsed gdistances!($g, $u, $dists)
    t_2 = @belapsed bfs_parents($g, $u)
    println("$t_1 $t_2;")
end

and then I calculated the relative speed-up for the graphs in gs before and after this pr:

 gdistances! bfs_parents
     0.99      0.99            --> path_graph(500)
     0.98      0.99            --> path_graph(5000)
     0.99      1.00            --> path_graph(50000)
     3.18      3.14            --> erdos_renyi(50, 0.5, seed=123)
    16.91      15.42           --> erdos_renyi(500, 0.5, seed=123)
   126.52      120.08          --> erdos_renyi(5000, 0.5, seed=123)
     5.40      5.19            --> complete_graph(50)
    46.14      40.11           --> complete_graph(500)
   512.26      475.42          --> complete_graph(5000)

The Path Graph is kind of the worst case scenario, and the time is approximately equal to the algorithm before this pr, but, as you can see, with a well connected Erdos Renyi the speed-up becomes very good, and finally I choose to benchmark a Complete Graph since it should be the best case scenario.

I also ran the tests locally and everything should still work!

[codecov]

Codecov Report

Merging #250 (1991e25) into master (53cb581) will decrease coverage by 0.02%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #250      +/-   ##
==========================================
- Coverage   97.23%   97.22%   -0.02%     
==========================================
  Files         114      114              
  Lines        6585     6595      +10     
==========================================
+ Hits         6403     6412       +9     
- Misses        182      183       +1     

[Tortar]

@gdalle If I can ask, what do you think about this PR? Since to me it seems a pretty good speed-up to have :-)

[etiennedeg]

Looks good to me

[simonschoelly]

This PR adds a heuristic that detects early that every vertex has been finished - it makes sense that it increases the speed in case of graphs with low diameter.

On the other hand, it adds some unnecessary if statements and a variable named k that could easily have been called something like num_visited. I think we should address such things in a code review instead of just merging them.

[etiennedeg]

The if statements are necessary, if some vertices are duplicated in source then k will be incremented too much.

[simonschoelly]

The if statements are necessary, if some vertices are duplicated in source then k will be incremented too much.

Ok thats a fair point.