Implement connectedComponents and isConnected #216
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@Synthetica9 Many thanks for the PR! I'm currently travelling and have a few other PRs to review, but I'll try to come back to you soon! |
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I did not had the opportunity to start working on this yet but since you presented your work I think the best thing is to use your code! Once I'm free from other academic tasks I can maybe we can go through this together :) |
Benchmarks
==========
These benchmarks were done with the following program:
```haskell
import Algebra.Graph (Graph)
import Algebra.Graph.NonEmpty (components, vertexCount)
import Algebra.Graph.Test.Arbitrary
import Data.Foldable
import qualified Data.Set as S
import Test.QuickCheck
import Test.QuickCheck.Gen
import Test.QuickCheck.Random
genSeed seed (MkGen g) =
do let r = mkQCGen seed
return (g r 30)
main :: IO ()
main = do
let gen = (resize 100 $ arbitrary) :: Gen (Graph Int)
for_ [1..1000] $ \seed -> do
g <- genSeed seed gen
print (vertexCount <$> (S.toList $ components g))
```
Ran on my own laptop. Not very scientific, but better than nothing, and
the improvement is clear.
The improvements mostly seem to be in the worst-case performance. When not
using a fixed seed, times varied drastically.
This does introduce a new dependency, but I think the speed improvement is
worth it.
5 graphs of depth 1000
----------------------
**New**
14.91user 0.04system 0:14.96elapsed 99%CPU (0avgtext+0avgdata 30688maxresident)k
0inputs+0outputs (0major+19991minor)pagefaults 0swaps
**Old**
188.67user 0.44system 3:09.12elapsed 99%CPU (0avgtext+0avgdata 31592maxresident)k
0inputs+0outputs (0major+18148minor)pagefaults 0swaps
12x improvement
1000 graphs of depth 100
------------------------
**New**
3.55user 0.02system 0:03.57elapsed 99%CPU (0avgtext+0avgdata
7408maxresident)k 0inputs+0outputs (0major+945minor)pagefaults 0swaps
**Old**
98.67user 0.21system 1:38.91elapsed 99%CPU (0avgtext+0avgdata
7352maxresident)k 0inputs+0outputs (0major+942minor)pagefaults 0swaps
27x improvement
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| Also see the autogenerated yet still possibly incomplete | ||
| [list of contributors](https://github.com/snowleopard/alga/graphs/contributors). | ||
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| Thank you all for your help! |
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| @@ -94,7 +94,8 @@ library | |||
| base >= 4.7 && < 5, | |||
| containers >= 0.5.5.1 && < 0.8, | |||
| deepseq >= 1.3.0.1 && < 1.5, | |||
| mtl >= 2.1 && < 2.3 | |||
| mtl >= 2.1 && < 2.3, | |||
| equivalence >= 0.3 && < 0.4 | |||
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I'd like to avoid introducing new dependencies.
Could you list the functionality you use along with asymptotic complexity?
| -- isConnected $ vertex x + vertex y == False | ||
| -- @ | ||
| isConnected :: Ord a => G.Graph a -> Bool | ||
| isConnected g = case Set.toList $ components g of |
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I guess you mean connected components in the sense of undirected graphs, right? If yes, this should be clarified and also moved to a more fitting module, e.g. Algebra.Graph.Undirected.Algorithm.
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@Synthetica9 It's been a while -- have you had a chance to look at the comments above? |
Based on #196.
I derived my own algorithm to get the connected components directly from the graph's structure. I'm not 100% on the complexity of it.
I'm also not 100% sure where these functions should go. They are intended for general graphs, but we can guarantee that every component isn't empty.
Also, there doesn't seem to be a place to put small tools that might be useful elsewhere, am I overlooking this?I was!src/Algebra/Graph/Internal.hscc @bolt12
(Did you get to this already? I couldn't find you work anywhere)TODO:
Set.disjointturns out to be fairly new. Backport?