hgraph (empty) → 1.2.0.0

raw patch · 29 files changed

+2323/−0 lines, 29 filesdep +HUnitdep +arraydep +base

Dependencies added: HUnit, array, base, clock, containers, happy-dot, hgraph, linear, mtl, random, transformers

Files

• ChangeLog.md +5/−0
• LICENSE +674/−0
• benchmarks/VertexCover.hs +35/−0
• hgraph.cabal +123/−0
• src/HGraph/Directed.hs +52/−0
• src/HGraph/Directed/AdjacencyMap.hs +51/−0
• src/HGraph/Directed/Connectivity.hs +138/−0
• src/HGraph/Directed/Load.hs +54/−0
• src/HGraph/Directed/Output.hs +43/−0
• src/HGraph/Directed/PathAnonymity.hs +78/−0
• src/HGraph/Directed/Subgraph.hs +74/−0
• src/HGraph/Undirected.hs +55/−0
• src/HGraph/Undirected/AdjacencyMap.hs +58/−0
• src/HGraph/Undirected/Expanders.hs +31/−0
• src/HGraph/Undirected/Generator.hs +67/−0
• src/HGraph/Undirected/Layout/SpringModel.hs +75/−0
• src/HGraph/Undirected/Load.hs +20/−0
• src/HGraph/Undirected/Output.hs +11/−0
• src/HGraph/Undirected/Solvers/IndependentSet.hs +46/−0
• src/HGraph/Undirected/Solvers/Treedepth.hs +88/−0
• src/HGraph/Undirected/Solvers/VertexCover.hs +56/−0
• src/HGraph/Utils.hs +4/−0
• tests/Digraph/Connectivity.hs +96/−0
• tests/Digraph/Load.hs +56/−0
• tests/Digraph/PathAnonymity.hs +91/−0
• tests/Digraph/Subgraph.hs +70/−0
• tests/Graph/AdjacencyMap.hs +33/−0
• tests/Graph/TestVertexCover.hs +78/−0
• tests/Graph/Treedepth.hs +61/−0

@@ -0,0 +1,5 @@+# Revision history for hgraph++## 1.0.0.0 -- 2019-06-07++* First version. 

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If not, see <http://www.gnu.org/licenses/>.++Also add information on how to contact you by electronic and paper mail.++  If the program does terminal interaction, make it output a short+notice like this when it starts in an interactive mode:++    <program>  Copyright (C) <year>  <name of author>+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.+    This is free software, and you are welcome to redistribute it+    under certain conditions; type `show c' for details.++The hypothetical commands `show w' and `show c' should show the appropriate+parts of the General Public License.  Of course, your program's commands+might be different; for a GUI interface, you would use an "about box".++  You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU GPL, see+<http://www.gnu.org/licenses/>.++  The GNU General Public License does not permit incorporating your program+into proprietary programs.  If your program is a subroutine library, you+may consider it more useful to permit linking proprietary applications with+the library.  If this is what you want to do, use the GNU Lesser General+Public License instead of this License.  But first, please read+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

@@ -0,0 +1,35 @@+{-# LANGUAGE BangPatterns #-}+module Main where++import HGraph.Undirected.Generator+import HGraph.Undirected.AdjacencyMap+import HGraph.Undirected.Solvers.VertexCover+import Data.List++import System.Clock+    +runBench !(g,name) = do+  start <- getTime ProcessCPUTime+  let vc = minimumVertexCover g+      !nVerts = numVertices g+      !nEdges = numEdges g+      !vcSize = length vc+  end <- getTime ProcessCPUTime+  let delta = (toNanoSecs $ diffTimeSpec end start) `div` 10^6 +  return $ ( intercalate ","+              [ show name+              , show nVerts+              , show nEdges+              , show delta+              , show vcSize+              ] ,+            delta)++instances = +  [ (grid emptyGraph w h, "grid-" ++ show w ++ "x" ++ show h) | w <- [1..8], h <- [w..8] ]++main = do+  results <- mapM runBench instances +  let times = map snd results+  let totalTime = sum times+  putStrLn $ intercalate "\n" $ "instance, vertices, edges, time (ms), solution" : map fst results

@@ -0,0 +1,123 @@+-- Initial hgraph.cabal generated by cabal init.  For further+-- documentation, see http://haskell.org/cabal/users-guide/++name:                hgraph+version:             1.2.0.0+synopsis:            Tools for working on (di)graphs.+-- description:+license:             GPL-3+license-file:        LICENSE+author:              Marcelo Garlet Milani+maintainer:          marcelogmillani@gmail.com+-- copyright:+category:            Data+build-type:          Simple+extra-source-files:  ChangeLog.md+cabal-version:       >=1.10++library+  exposed-modules: HGraph.Directed, HGraph.Directed.AdjacencyMap HGraph.Directed.Connectivity+                   HGraph.Directed.Load+                   HGraph.Directed.Output+                   HGraph.Directed.PathAnonymity+                   HGraph.Directed.Subgraph+                   HGraph.Undirected, HGraph.Undirected.AdjacencyMap+                   HGraph.Undirected.Solvers.VertexCover+                   HGraph.Undirected.Solvers.Treedepth+                   HGraph.Undirected.Solvers.IndependentSet+                   HGraph.Undirected.Generator+                   HGraph.Undirected.Expanders+                   HGraph.Undirected.Load+                   HGraph.Undirected.Layout.SpringModel+                   HGraph.Undirected.Output+  other-modules:   HGraph.Utils+  default-extensions:  TypeSynonymInstances, DoAndIfThenElse, GADTs+  build-depends:       base >=4.11 && <5, containers >= 0.5, happy-dot >= 0.1, transformers >= 0.5, mtl, random, linear >= 1.21, array >= 0.5+  hs-source-dirs:      src+  default-language:    Haskell2010++source-repository head+  type:     git+  location: git@gitlab.com:mgmillani/hgraph.git++--library hgraph-lib+--  exposed-modules: HGraph.Directed, HGraph.Directed.AdjacencyMap, HGraph.Directed.Connectivity+--                   HGraph.Directed.Load+--                   HGraph.Output+--                   HGraph.Undirected, HGraph.Undirected.AdjacencyMap+--                   HGraph.Undirected.Solvers.VertexCover+--                   HGraph.Undirected.Solvers.Treedepth+--                   HGraph.Undirected.Generator+--                   HGraph.Undirected.Expanders+--                   HGraph.Undirected.Load+--                   HGraph.Undirected.Layout.SpringModel+--  -- other-modules:+--  default-extensions:  TypeSynonymInstances, DoAndIfThenElse, GADTs+--  build-depends:       base >=4.11 && <5, containers >= 0.5, happy-dot >= 0.1, transformers >= 0.5, mtl, random, linear >= 1.21, array >= 0.5+--  hs-source-dirs:      src+--  default-language:    Haskell2010+++--executable hgraph-viewer+--  main-is:             Main.hs+--  other-modules:       HGraph.Simulation HGraph.Geometry+--  -- other-extensions:+--  build-depends:       base >=4.8 && <5, transformers >= 0.5, containers >= 0.5.9, directory >= 1.3, hgraph-lib, OpenGL >= 3.0, linear >= 1.21, bytestring >= 0.10, vector >= 0.11, sdl2 >= 2.1 +--  hs-source-dirs:      viewer+--  default-language:    Haskell2010++test-suite test-adjacency-map+  main-is:          AdjacencyMap.hs+  hs-source-dirs:   tests/Graph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++test-suite test-vertex-cover+  main-is:          TestVertexCover.hs+  hs-source-dirs:   tests/Graph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++Benchmark bench-vertex-cover+  main-is:          VertexCover.hs+  hs-source-dirs:   benchmarks+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, containers >= 0.5, transformers >= 0.5, clock >= 0.7, hgraph, random+  default-language: Haskell2010++test-suite test-treedepth+  main-is:          Treedepth.hs+  hs-source-dirs:   tests/Graph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++test-suite test-connectivity+  main-is:          Connectivity.hs+  hs-source-dirs:   tests/Digraph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++test-suite test-path-anonymity+  main-is:          PathAnonymity.hs+  hs-source-dirs:   tests/Digraph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++test-suite test-subgraph+  main-is:          Subgraph.hs+  hs-source-dirs:   tests/Digraph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010++test-suite test-load+  main-is:          Load.hs+  hs-source-dirs:   tests/Digraph+  type:             exitcode-stdio-1.0+  build-depends:    base >=4.11 && <5, transformers >= 0.5, containers >= 0.5.9, HUnit >= 1.6, hgraph+  default-language: Haskell2010

@@ -0,0 +1,52 @@+{-# LANGUAGE GADTs #-}++module HGraph.Directed+       ( DirectedGraph(..)+       , Adjacency(..)+       , Mutable(..)+       )+where++import qualified Data.Map as M+import qualified Data.Set as S++class DirectedGraph t where+  empty :: t a -> t a+  vertices :: t a -> [a]+  numVertices :: Integral b => t a -> b+  numVertices d = fromIntegral $ length $ vertices d+  arcs :: t a -> [(a,a)]+  numArcs :: Integral b => t a -> b+  numArcs d = fromIntegral $ length $ arcs d+  linearizeVertices :: t a -> (t Int, [(Int, a)])+  isVertex :: t a -> a -> Bool++class Adjacency t where+  outneighbors :: t a -> a -> [a]+  inneighbors  :: t a -> a -> [a]+  outdegree :: Integral b => t a -> a -> b+  outdegree d v = fromIntegral $ length $ outneighbors d v+  indegree :: Integral b => t a -> a -> b+  indegree d v = fromIntegral $ length $ inneighbors d v+  arcExists :: t a -> (a,a) -> Bool+  metaBfs :: Ord a => t a -> a -> ([a] -> [a]) -> ([a] -> [a]) -> [a]+  metaBfs d v inFilter outFilter =+    metaBfs' S.empty (S.fromList $ (inFilter $ inneighbors d v) ++ (outFilter $ outneighbors d v))+    where+      metaBfs' visited toVisit = +        let vs = S.toList toVisit+            newToVisit =+              (S.unions $ map+                (S.fromList . +                  (\v -> (inFilter $ inneighbors d v) ++ (outFilter $ outneighbors d v)))+                vs+              )+              `S.difference` visited+        in if S.null newToVisit then vs else vs ++ metaBfs' (S.union (S.fromList vs) visited) newToVisit++class Mutable t where+  addVertex    :: a -> t a -> t a+  removeVertex :: a -> t a -> t a+  addArc    :: (a,a) -> t a -> t a+  removeArc :: (a,a) -> t a -> t a+

@@ -0,0 +1,51 @@+module HGraph.Directed.AdjacencyMap+       ( Digraph+       , emptyDigraph+       , module HGraph.Directed+       )+where++import HGraph.Directed+import qualified Data.Map as M+import qualified Data.Set as S++type DirectedNeighborhood a = (S.Set a, S.Set a)+data Digraph a where+  Digraph :: Ord a => M.Map a (DirectedNeighborhood a) -> Digraph a++emptyDigraph :: Ord a => Digraph a+emptyDigraph = Digraph M.empty++instance DirectedGraph Digraph where+  empty (Digraph d) = Digraph M.empty+  numVertices (Digraph d) = fromIntegral $ M.size d+  vertices (Digraph d) = M.keys d+  arcs (Digraph d) = concatMap (\(v, (_,o)) -> [(v,u) | u <- S.toList o]) $ M.assocs d+  isVertex (Digraph d) v = v `M.member` d+  linearizeVertices g@(Digraph adj) = (g', assocs)+    where+      assocs = zip [0..] (M.keys adj)+      ltoi = M.fromList $ zip (M.keys adj) [0..]+      g' = foldr addArc (foldr addVertex emptyDigraph (map fst assocs)) $+            [ (ltoi M.! u, ltoi M.! v) | (u,v) <- arcs g ]++instance Adjacency Digraph where+  outneighbors (Digraph d) v = S.toList $ snd $ d M.! v+  inneighbors  (Digraph d) v = S.toList $ fst $ d M.! v+  arcExists (Digraph d) (v,u) = u `S.member` (snd $ d M.! v)++instance Mutable Digraph where+  addVertex v (Digraph d) =+    Digraph (M.insertWith (\_ o -> o) v (S.empty, S.empty) d)+  removeVertex v g@(Digraph d) = +      let Digraph d' = foldr removeArc g+                     (  (map (\u -> (v,u)) $ outneighbors g v)+                     ++ (map (\u -> (u,v)) $ inneighbors  g v))+      in Digraph $ M.delete v d'+            +  addArc (v,u) (Digraph d) =+    Digraph ( M.adjust (\(i,o) -> (i, S.insert u o)) v+            $ M.adjust (\(i,o) -> (S.insert v i, o)) u d)+  removeArc (v,u) (Digraph d)  =+    Digraph ( M.adjust (\(i,o) -> (i, S.delete u o)) v+            $ M.adjust (\(i,o) -> (S.delete v i, o)) u d)

@@ -0,0 +1,138 @@+module HGraph.Directed.Connectivity+       ( reachable+       , allPaths+       , allLinkages+       , allMaximalPaths+       , extendLinkage+       , LinkageInstance(..)+       , module F+       , module IL+       )+where++import Data.List+import HGraph.Directed+import HGraph.Directed.Connectivity.Flow as F+import HGraph.Directed.Connectivity.IntegralLinkage as IL+import qualified Data.Map as M+import qualified Data.Set as S+import Control.Monad++--data LinkageInstance a = +--  LinkageInstance+--  { liTerminalPairs :: M.Map Int (a,a)+--  , liCapacities :: M.Map a Int+--  , liLinkage :: M.Map a (S.Set Int)+--  }++--extendLinkage d inst = +--  case extendLinkage' $ M.keys $ liTerminalPairs inst of+--    Nothing -> Nothing+--    Just [] -> Just inst+--    Just ext ->+--      let link' = M.union (foldr (\(v,i) -> +--                                   M.insertWith S.union v (S.singleton i))+--                                 M.empty ext)+--                          (liLinkage inst)+--          st' = M.union (M.fromList $ [ (i, (v, t))+--                                    | (v,i) <- ext+--                                    , let (s,t) = (liTerminalPairs inst) M.! i+--                                    , v `elem` (outneighbors d s)+--                                    ] +++--                                    [ (i, (s, v))+--                                    | (v,i) <- ext+--                                    , let (s,t) = (liTerminalPairs inst) M.! i+--                                    , v `elem` (inneighbors d t)+--                                    ]+--                        )+--                        (liTerminalPairs inst)+--      in extendLinkage d inst{liTerminalPairs = st', liLinkage = link'}+--  where+--    extendLinkage' [] = Just []+--    extendLinkage' (i:is)+--      | s == t  = extendLinkage' is+--      | null cut = Nothing+--      | not $ null $ drop 1 cut = extendLinkage' is+--      | not $ i `S.member` ((liLinkage inst) M.! cv)  = Just [(cv,i)]+--      where+--        (s,t) = (liTerminalPairs inst) M.! i+--        d' = foldr removeVertex d+--                   [ v+--                   | (v,w) <- M.assocs $ liCapacities inst+--                   , (not $ i `elem` (liLinkage inst) M.! v) && w == (S.size $ (liLinkage inst) M.! v)+--                   ]+--        cut = minCutI d' s t+--        cv = head cut++reachable d s t = t `elem` (metaBfs d s (\_ -> []) id)++allPaths d s t = allPaths' S.empty s+  where+    allPaths' visited s+      | s == t = [[t]]+      | otherwise = do+        v <- filter (\u -> not $ u `S.member` visited) $ outneighbors d s+        fmap (s:) $ allPaths' (S.insert v visited) v++allLinkages+  :: (DirectedGraph t1, Adjacency t1, Eq b, Eq t2, Num t2)+  => t1 b -> t2 -> b -> b -> [[[b]]]+allLinkages d k s t = do+  s0 <- choose k (outneighbors di si)+  fmap (map ((s :) . map (iToV M.!))) $ allLinkages' s0 (S.fromList $ si : s0)+  where+    (di, itova) = linearizeVertices d+    Just si = fmap fst $ find ((==s) . snd) itova+    Just ti = fmap fst $ find ((==t) . snd) itova+    iToV = M.fromList itova+    allLinkages' si visited+      | all (==ti) si = return $ map (:[]) si+      | otherwise = do+      (step, visited') <- linkageSteps di visited si ti+      fmap (zipWith (:) si) $ allLinkages' step visited'++linkageSteps d visited [] t = return ([], visited)+linkageSteps d visited (v:vs) t = do+  u <- if v == t then return v else filter (\u -> not $ S.member u visited) $ outneighbors d v+  fmap (\(ws, visited') -> (u:ws, visited')) $ linkageSteps d (if u /= t then S.insert u visited else visited) vs t++-- | All maximal paths on a digraph, represented as a list of vertices.+-- | Cycles are also considered as maximal paths and their corresponding lists contain the initial vertex twice.+allMaximalPaths d = map (map (iToV M.!)) $ allMaximalPaths' (vertices di) S.empty+  where+    (di, itova) = linearizeVertices d+    iToV = M.fromList itova+    allMaximalPaths' [] _ = []+    allMaximalPaths' (v:vs) blocked = vPaths ++ allMaximalPaths' vs (S.insert v blocked)+      where+        vPaths = concatMap inExtensions $ uniPaths True outneighbors blocked v+        uniPaths canClose neighborF visited u+          | null nu && (null $ filter (`S.member` blocked) $ neighborF di u) = [[u]]+          | null nu && null vCycle = []+          | null nu = [[u, v]]+          | otherwise = map (u:) $ vCycle ++ concatMap (uniPaths canClose neighborF (S.insert u visited)) nu+          where+            nu = filter (not . (`S.member` visited)) $ neighborF di u+            vCycle+              | not canClose = []+              | v `elem` (neighborF di u) = [[v]]+              | otherwise = []+        inExtensions p +          | p0 == pn && (not $ null $ drop 1 p) = [p] -- p is already a cycle+          | otherwise = map combine $ uniPaths canClose inneighbors (foldr S.insert blocked p) v+          where+            canClose = null $ drop 1 p -- allow closing backwards cycles+            combine q+              | null q = []+              | arcExists di (pn, q0) = pn : q' ++ p+              | null q' = p +              | otherwise = q' ++ p+              where+                q' = reverse $ tail q+                q0 = last q+            pn = last p+            p0 = head p++choose 0 _  = [[]]+choose k [] = []+choose k (x:xs) = map (x:) (choose (k - 1) xs) ++ choose k xs

@@ -0,0 +1,54 @@+module HGraph.Directed.Load+       ( loadDot+       , loadEdgeList+       )+where++import HGraph.Directed+import HGraph.Utils+import qualified Language.Dot.Parser as D+import qualified Language.Dot.Utils as D+import qualified Language.Dot.Graph  as D+import qualified Data.Map as M+import qualified Data.Set as S+import Data.Maybe+import Text.Read++loadDot emptyD dotStr = do+  dot <- D.parse dotStr+  return $ +    let (ns, es) = D.adjacency dot+        names = (S.toList $ S.fromList $ map getNodeName ns)+        nid = M.fromList $ zip names ([0..] :: [Int])+        idToStr = M.fromList $ zip ([0..] :: [Int]) names+        addEdge (D.Edge v u _) d = addArc (nid M.! v, nid M.! u) d+        getNodeName (D.Node name _) = name+        nodeAttrMap = M.fromList [ (v, attrs) | D.Node v attrs <- ns]+        edgeAttrMap = M.fromList [ ((v,u), attrs) | D.Edge v u attrs <- es]+    in (foldr addEdge (foldr addVertex emptyD $ M.keys idToStr) es, nid, idToStr, nodeAttrMap, edgeAttrMap)++loadEdgeList emptyD dStr+  | null terms = return emptyD+  | otherwise = do+    nv <- fromMaybe (Left "Invalid number of vertices.") $ do+          t0 <- mhead terms+          n <- readMaybe t0+          if n < 1 then Nothing else return $ Right n+    ne <- fromMaybe (Left "Invalid number of edges.") $ do+          t0 <- mhead $ drop 1 terms+          e <- readMaybe t0+          if e < 0 then Nothing else return $ Right e+    es <- readEdges nv $ drop 2 terms+    if ne /= (length es) then+      Left $ "Expected " ++ (show ne) ++ " many edges, found " ++ (show $ length es) ++ "."+    else+      return $ foldr addArc (foldr addVertex emptyD [0..nv - 1]) es+  where+    terms = words dStr+    readEdges _ [] = return []+    readEdges _ [_] = Left "Missing tail of last edge."+    readEdges nv (vStr:uStr:vs) = do+      v <- fromMaybe (Left $ "Invalid vertex: " ++ vStr) $ fmap Right $ readMaybe vStr+      u <- fromMaybe (Left $ "Invalid vertex: " ++ uStr) $ fmap Right $ readMaybe uStr+      fmap ((v `mod` nv, u `mod` nv) : ) (readEdges nv vs)+

@@ -0,0 +1,43 @@+module HGraph.Directed.Output+  ( toDot+  , DotStyle(..)+  , defaultDotStyle+  )+where++import HGraph.Directed+import Data.List+import qualified Data.Map as M++data DotStyle a = +  DotStyle+  { graphName :: String+  , everyNode :: [(String, String)]+  , everyEdge :: [(String, String)]+  , nodeAttributes :: M.Map a [(String, String)]+  , edgeAttributes :: M.Map (a, a) [(String, String)]+  }++defaultDotStyle = DotStyle+  { graphName = ""+  , everyNode = []+  , everyEdge = []+  , nodeAttributes = M.empty+  , edgeAttributes = M.empty+  }++toDot d style = concat+  [ "digraph ", (graphName style), "{\n  "+  , if null $ everyNode style then "" else "node [" ++ attStr (everyNode style) ++ "];\n  "+  , if null $ everyEdge style then "" else "edge [" ++ attStr (everyEdge style) ++ "];\n  "+  , intercalate ";\n  " (map showV $ vertices d),  ";\n  "+  , intercalate ";\n  " (map showA $ arcs d) , ";\n}"+  ]+  where+    attStr xs = intercalate "," $ map (\(var,val) -> var ++ "=\"" ++ val ++ "\"") xs+    showV v+      | v `M.member` (nodeAttributes style) = show v ++ " [" ++ attStr ((nodeAttributes style) M.! v) ++ "]"+      | otherwise = show v+    showA (v,u)+      | (v,u) `M.member` (edgeAttributes style) = show v ++ " -> " ++ show u ++ " [" ++ attStr ((edgeAttributes style) M.! (v,u)) ++ "]"+      | otherwise = show v ++ " -> " ++ show u

@@ -0,0 +1,78 @@+module HGraph.Directed.PathAnonymity+       ( pathAnonymity+       , pathAnonymityCertificate+       , pathPathAnonymityI+       )+where++import HGraph.Directed+import HGraph.Directed.Connectivity+import qualified Data.Map as M+import qualified Data.Set as S+import Data.List++pathAnonymity d = snd $ pathAnonymityCertificate d++-- | Path anonymity of a digraph together with a path witnessing+-- | that the anonymity is at least the returned value.+pathAnonymityCertificate d = (map (iToV M.!) p, k)+  where+    (p,k) = pathAnonymityCertificateI di+    (di, itova) = linearizeVertices d+    iToV = M.fromList itova++pathAnonymityCertificateI di =+  maximumBy (\(_,k1) (_,k2) -> compare k1 k2) $+    map (\p -> (p, pathPathAnonymityI di p)) $+        allMaximalPaths di++-- | Path anonymity of a maximal path.+-- | The path provided is assumed to be maximal.+pathPathAnonymityI di p+  | null $ drop 1 p = 0+  | otherwise = numCriticalPaths p +  where+    ps = S.fromList p+    pI = foldr (\(k,i) -> M.insertWith (\o _ -> o) k i) M.empty $ zip p [0..]+    pr = reverse p+    isCycle = take 1 p == take 1 pr+    f0 = head p+    mn+      | isCycle   = head $ drop 1 pr+      | otherwise = head pr+    m0 = take 1 $ dropWhile (\v -> null $ filter (not . (`S.member` ps)) (inneighbors di v)) p+    fn = take 1 $ dropWhile (\v -> null $ filter (not . (`S.member` ps)) (outneighbors di v)) $+          (if isCycle then tail else id) $ pr+    vF+      | isCycle && ((not $ null fn) || (not $ null m0)) =+                    S.fromList $ fn ++ (mn : f0 : map fst shortcutPairs)+      | otherwise = S.fromList $ fn ++ (f0 : map fst shortcutPairs)+    vM+      | isCycle && ((not $ null m0) || (not $ null fn)) = +                    S.fromList $ m0 ++ (f0 : mn : map snd shortcutPairs)+      | otherwise = S.fromList $ m0 ++ (mn : map snd shortcutPairs)+    shortcuts v = filter (\(u,w) -> pI M.! u < pI M.! w) $ shortcuts' di ps v+    shortcutPairs = concatMap (\v -> shortcuts v ++ directShortcuts v) p+    directShortcuts v = filter (\(u,w) -> pI M.! u + 1 < pI M.! w) $ directShortcuts' di ps v+    numCriticalPaths = numCriticalPaths' vF vM++numCriticalPaths' _ _ [] = 0+numCriticalPaths' vF vM (_:vs)+  | null vm = 0+  | otherwise = 1 + numCriticalPaths' vF vM vs'+  where+    vm  = dropWhile (not . (`S.member` vM)) vs+    vs' = dropWhile (not . (`S.member` vF)) vm+        +shortcuts' di blocked v =+  [ (v,w)+  | u <- us+  , w <- filter (`S.member` blocked) $ outneighbors di u+  ]+  where+    us = metaBfs di v (\_ -> []) (filter (not . (`S.member` blocked)))++directShortcuts' di blocked v = [ (v,w)+     | w <- outneighbors di v+     , w `S.member` blocked+     ]

@@ -0,0 +1,74 @@+module HGraph.Directed.Subgraph+       ( contains+       , isSubgraphOf+       , subgraphIsomorphism+       , subgraphIsomorphismI+       , isSubgraphIsomorphism+       )+where++import HGraph.Directed+import HGraph.Utils+import qualified Data.Map as M+import qualified Data.Set as S+import Data.Maybe++-- | Whether `d` contains `h` as a subgraph (the identity is used for the isomorphism).+contains d h = null $ +  [ v+  | v <- vertices h+  , u <- outneighbors h v+  , not $ arcExists d (v,u)+  ] +++  filter (not . isVertex d) (vertices h)+  ++-- | Whether `h` is isomorphic to some subgraph of `d`.+isSubgraphOf h d = isJust $ subgraphIsomorphism d h++-- | Find an isomorphism from `h` to some subgraph of `d`, if it exists.+subgraphIsomorphism d h = fmap (M.mapKeys (iToV M.!)) $ subgraphIsomorphismI d hi+  where+    (hi, itova) = linearizeVertices h+    iToV = M.fromList itova++subgraphIsomorphismI d hi = findIso (vertices hi) M.empty candidates0+  where+    candidates0 = M.fromList+                  [ (v, S.fromList us)+                  | v <- vertices hi+                  , let ov = outdegree hi v+                  , let iv = indegree hi v+                  , let us = filter (\u -> outdegree d u >= ov && indegree d u >= iv) $ vertices d+                  ]+    findIso [] phi _ = Just phi+    findIso (v:vs) phi candidates = mhead $ map fromJust $ filter isJust $ do      +      u <- S.toList $ candidates M.! v+      let phi' = M.insert v u phi+      let candidates' = M.map (S.delete u) $ M.delete v $ +              foldr (uncurry $ M.insertWith (\n o -> S.intersection n o) )+                    candidates $+                    [ (w, S.fromList $ outneighbors d u)+                    | w <- outneighbors hi v+                    ] +++                    [ (w, S.fromList $ inneighbors d u)+                    | w <- inneighbors hi v+                    ]+      if null $ M.filter S.null candidates' then+        return $ findIso vs phi' candidates'+      else+        []++-- | Whether `phi` is a subgraph isomorphism from `h` to some subgraph of `d`.+isSubgraphIsomorphism d h phi = null+  [ v+  | v <- vertices h+  , u <- outneighbors h v+  , isNothing $ do+      dv <- M.lookup v phi+      du <- M.lookup u phi+      if arcExists d (dv,du) then+        return ()+      else+        Nothing+  ]

@@ -0,0 +1,55 @@+{-# LANGUAGE GADTs #-}++module HGraph.Undirected+       ( UndirectedGraph(..)+       , Adjacency(..)+       , Mutable(..)+       )+where++import qualified Data.Set as S++class UndirectedGraph t where+  empty :: t a -> t a+  vertices :: t a -> [a]+  numVertices :: Integral b => t a -> b+  numVertices d = fromIntegral $ length $ vertices d+  edges :: t a -> [(a,a)]+  numEdges :: Integral b => t a -> b+  numEdges d = fromIntegral $ length $ edges d+  linearizeVertices :: t a -> (t Int, [(Int, a)])++class UndirectedGraph t => Adjacency t where+  neighbors :: t a -> a -> [a]+  degree :: Integral b => t a -> a -> b+  edgeExists :: t a -> (a,a) -> Bool+  inducedSubgraph :: t a -> [a] -> t a+  metaBfs :: Ord a => t a -> a -> ([a] -> [a]) -> [a]+  metaBfs d v nFilter =+    v : metaBfs' (S.singleton v) (S.fromList $ (nFilter $ neighbors d v))+    where+      metaBfs' visited toVisit = +        let vs = S.toList toVisit+            newToVisit =+              (S.unions $ map+                (S.fromList . +                  (\v -> (nFilter $ neighbors d v)))+                vs+              )+              `S.difference` visited+        in if S.null newToVisit then vs else vs ++ metaBfs' (S.union (S.fromList vs) visited) newToVisit+  connectedComponents :: Ord a => t a -> [[a]]+  connectedComponents g = cc (vertices g) S.empty+    where+      cc [] _ = []+      cc (v:vs) visited+        | v `S.member` visited = cc vs visited+        | otherwise = component : cc vs (S.union visited $ S.fromList component)+        where+          component = metaBfs g v id++class Mutable t where+  addVertex    :: t a -> a -> t a+  removeVertex :: t a -> a -> t a+  addEdge    :: t a -> (a,a) -> t a+  removeEdge :: t a -> (a,a) -> t a

@@ -0,0 +1,58 @@+{-# LANGUAGE GADTs #-}++module HGraph.Undirected.AdjacencyMap+       ( Graph+       , emptyGraph+       , module HGraph.Undirected+       )+where++import HGraph.Undirected+import qualified Data.Map as M+import qualified Data.Set as S++data Graph a where+  Graph :: Ord a => M.Map a (S.Set a) -> Int -> Graph a++emptyGraph :: Ord a => Graph a+emptyGraph = Graph M.empty 0++instance UndirectedGraph Graph where+  empty (Graph _ _) = Graph M.empty 0+  vertices (Graph adj _) = M.keys adj+  numVertices (Graph adj _) = fromIntegral $ M.size adj+  edges (Graph adj _) = [(v,u) | (v, nv) <- M.assocs adj, u <- S.toList nv, u >= v]+  numEdges (Graph _ numE) = fromIntegral $ numE+  linearizeVertices g@(Graph adj _) = (g', assocs)+    where+      assocs = zip [0..] (M.keys adj)+      ltoi = M.fromList $ zip (M.keys adj) [0..]+      g' = foldr (flip addEdge) (foldr (flip addVertex) emptyGraph (map fst assocs)) $+            [ (ltoi M.! u, ltoi M.! v) | (u,v) <- edges g ]+++instance Adjacency Graph where+  neighbors (Graph adj _) v = S.toList $ adj M.! v+  degree (Graph adj _) v = fromIntegral $ S.size $ adj M.! v+  edgeExists (Graph adj _) (v,u) = u `S.member` (adj M.! v)+  inducedSubgraph (Graph adj numE) vs = Graph adj' $ (M.foldl' (\s n -> s + S.size n) 0 adj') `div` 2+    where+      adj' = M.map (\n -> S.intersection n svs) $ M.restrictKeys adj svs+      svs = S.fromList vs++instance Mutable Graph where+  addVertex (Graph adj nE) v = Graph (M.insert v S.empty adj) nE+  removeVertex g@(Graph adj nE) v = +    Graph (M.delete v $ foldr (M.adjust (S.delete v)) adj nv) (nE - (degree g v))+    where+      nv = neighbors g v+  addEdge g@(Graph adj nE) (v,u)+    | edgeExists g (v,u) = g+    | otherwise = Graph adj' (nE + 1)+      where+        adj' = M.insertWith S.union v (S.singleton u) $ M.insertWith S.union u (S.singleton v) adj+  removeEdge g@(Graph adj nE) (v,u)+    | not $ edgeExists g (v,u) = g+    | otherwise = Graph adj' (nE - 1)+      where+        adj' = M.adjust (S.delete u) v $ M.adjust (S.delete v) u adj

@@ -0,0 +1,31 @@+module HGraph.Undirected.Expanders+       ( edgeExpansion+       , vertexExpansion+       )+where++import HGraph.Undirected+import qualified Data.Map as M++edgeExpansion :: (UndirectedGraph g, Adjacency g) => g a -> (Double, [a])+-- | Edge expansion of a graph, together with a set of verticies certifying that the expansion is not greater.+edgeExpansion g = (expansion, cert)+  where+    (expansion, cert') = edgeExpansion' (numVertices gi `div` 2) (vertices gi) []+    cert = map (idT M.!) cert'+    (gi, itol) = linearizeVertices g+    idT = M.fromList itol+    edgeExpansion' budget [] [] = (fromIntegral $ numVertices gi, [])+    edgeExpansion' budget [] as = (fromIntegral e / (fromIntegral $ length as), as)+      where+        e = sum [degree gi v | v <- as]+    edgeExpansion' 0 _ as = edgeExpansion' 0 [] as+    edgeExpansion' budget (v:vs) as = (e, c)+      where+        (e0,c0) = edgeExpansion' (budget - 1) vs (v : as)+        (e1,c1) = edgeExpansion' budget vs as+        (e,c) = if e0 < e1 then (e0,c0) else (e1,c1)++vertexExpansion :: (Adjacency g) => g a -> (Double, [a])+-- | Vertex expansion of a graph, together with a set of verticies certifying that the expansion is not greater.+vertexExpansion g = (0,[])

@@ -0,0 +1,67 @@+module HGraph.Undirected.Generator+       ( grid+       , cycleGraph+       , completeTree+       , completeGraph+       , randomGraph+       )+where++import HGraph.Undirected+import Data.List+import Control.Monad.State+import System.Random++cycleGraph g0 n = foldr (flip addEdge) (foldr (flip addVertex) g0 [0..n-1]) [(x, (x + 1) `mod` n) | x <- [0..n-1]]++grid g0 w h = foldr (flip addEdge) (foldr (flip addVertex) g0 vs) es+  where+    vs = [(x,y) | x <- [1..w], y <- [1..h]]+    es = concat [[(v,(x+1,y)), (v, (x,y+1))] | x <- [1..w-1], y <- [1..h-1], let v = (x,y)]+      ++ [((x, h), (x+1, h)) | x <- [1..w-1]]+      ++ [((w, y), (w, y+1)) | y <- [1..h-1]]++completeTree g0 depth arity = completeTree' (addVertex (empty g0) 0) 0 1+  where+    completeTree' g root d+      | d > depth = g+      | otherwise = head $ drop arity $+                    iterate' (\h -> let r1 = numVertices h+                                   in addEdge (completeTree' (addVertex h r1) r1 (d+1) ) (root,r1)) g++completeGraph g0 k = foldr (flip addEdge) (foldr (flip addVertex) (empty g0) [0..k-1]) [(u,v) | u <- [0..k-1], v <- [u+1..k-1] ]++randomGraph g0 n m+  | m > (n * (n - 1)) `div` 4 = do -- dense graph+    let g1 = foldr (flip addEdge) (foldr (flip addVertex) (empty g0) [1..n]) [(v,u) | v <- [1..n], u <- [v+1..n]]+    removeRandomEdges g1 m+  | otherwise = do -- spare graph+    let g1 = foldr (flip addVertex) (empty g0) [0..n-1]+    addRandomEdges g1 m++addRandomEdges g m+  | numEdges g == m = return g+  | otherwise = do+    v <- randomN 0 (numVertices g - 1)+    u <- randomN 0 (numVertices g - 1)+    if u /= v then+      addRandomEdges (addEdge g (v,u)) m+    else+      addRandomEdges g m++removeRandomEdges g m+  | numEdges g == m = return g+  | otherwise = do+    v <- randomN 0 (numVertices g - 1)+    u <- randomN 0 (numVertices g - 1)+    if u /= v && edgeExists g (v,u) then+      removeRandomEdges (removeEdge g (v,u)) m+    else+      removeRandomEdges g m++randomN :: (Random a, RandomGen g) => a -> a -> State g a+randomN n0 n1 = do+  gen <- get+  let (r,gen') = randomR (n0,n1) gen+  put gen'+  return r

@@ -0,0 +1,75 @@+module HGraph.Undirected.Layout.SpringModel+        (setup, step, positions)+where++import HGraph.Undirected+import qualified Data.Array.Unboxed as U+import qualified Data.Map as M+import Data.Foldable+import Linear++data SpringModel g a = +  SpringModel+  { smGraph :: g Int+  , smPoints :: U.Array Int (V2 Double)+  , smVelocities :: U.Array Int (V2 Double)+  , smSpringStrength    :: Double+  , smRepulsionStrength :: Double+  , smFriction :: Double+  , smCenterAttractionStrength :: Double+  , smIndexToLabel :: M.Map Int a+  }++setup centerAttraction springStrength repulsiveStrength friction gr =+  let (gi, itol) = linearizeVertices gr+      n = numVertices gi - 1+  in SpringModel+  { smGraph = gi+  , smPoints = U.array (0, n) $ zip [0..n] (repeat 0)+  , smVelocities = U.array (0, n) $ zip [0..n] (repeat 0)+  , smSpringStrength = springStrength+  , smRepulsionStrength = repulsiveStrength+  , smFriction = friction+  , smCenterAttractionStrength = centerAttraction+  , smIndexToLabel = M.fromList itol+  }++step dt layout = layout{smPoints = points', smVelocities = velocities'}+  where+    points = smPoints layout+    velocities = smVelocities layout+    points' = U.array (U.bounds points)+      [ (i, (points U.! i) + (velocities U.! i))+      | i <- U.indices points +      ]+    velocities' = U.array (U.bounds points)+                          [ (i, ((smFriction layout) ** dt) *^ (velocities U.! i) + (accelerate layout i))+                          | i <- U.indices $ points]++accelerate layout v = springV ^+^ centerV ^+^ pushV+  where+    positions = smPoints layout+    pv = positions U.! v+    springV = sum+      [ du ^* (smSpringStrength layout)+      | u <- neighbors (smGraph layout) v+      , let pu = positions U.! u+      , let du = pu ^-^ pv+      ]+    centerV = (negated pv) ^* (smCenterAttractionStrength layout)+    pushV = sum+      [ if d2 < 0.0001 then+           (100 * smRepulsionStrength layout) *^ (angle $ 2*pi * ((fromIntegral v) / (fromIntegral $ U.rangeSize $ U.bounds positions)))+        else+           ((du ^/ (sqrt d2)) ^* (smRepulsionStrength layout)) ^/ d2+      | u <- vertices $ smGraph layout+      , let pu = positions U.! u+      , let du = pv ^-^ pu+      , let d2 = foldl' (\s x -> s + x*x) 0 du+      , u /= v+      ]++positions layout =+  [ (smIndexToLabel layout M.! i, (smPoints layout) U.! i)+  | i <- U.indices $ smPoints layout+  ]

@@ -0,0 +1,20 @@+module HGraph.Undirected.Load+       ( loadDot+       )+where++import HGraph.Undirected+import Language.Dot.Parser as D+import Language.Dot.Utils  as D+import Language.Dot.Graph  as D+import qualified Data.Map  as M+import qualified Data.Set  as S++loadDot gr dotStr = do+  dot <- D.parse dotStr+  return $ +    let (ns, es) = D.adjacency dot+        names = (S.toList $ S.fromList $ map getNodeName ns)+        addE (D.Edge v u _) d = addEdge d (v, u)+        getNodeName (D.Node name _) = name+    in foldr addE (foldr (flip addVertex) gr names) es

@@ -0,0 +1,11 @@+module HGraph.Undirected.Output+  ( toDot+  )+where++import HGraph.Undirected+import Data.List++toDot g = "graph {\n  "+  ++ intercalate ";\n  " (map show $ vertices g) ++ ";\n"+  ++ intercalate ";\n  " (map (\(v,u) -> show v ++ " -- " ++ show u) $ edges g) ++ ";\n}"

@@ -0,0 +1,46 @@+module HGraph.Undirected.Solvers.IndependentSet+        ( maximize+        , atLeast+        , reduce+        )+where++import Data.Maybe+import HGraph.Undirected+import HGraph.Utils++-- | Find a maximum independet set in `g`+maximize g = last [fromJust x | k <- [1..numVertices g], let x = atLeast g k, isJust x]++-- | Search for an independent set of size at least `k` in `g`+atLeast g k+  | k <= 0 = Just []+  | numVertices g == 0 = Nothing+  | otherwise = +    let (g', xs, k') = reduce g k+    in+    if k' >= k then+      Just xs+    else+      fmap (xs ++) $ +        mhead [ u : fromJust ys+              | u <- vertices g'+              , let ys = atLeast (foldr (flip removeVertex) g' $ u : neighbors g' u) (k - 1 - k')+              , isJust ys]++reduce g k+  | k <= 0 = (g, [], 0)+  | k > (numVertices g) || (k == (numVertices g) && numEdges g > 0) = (empty g, [], 0)+  | otherwise = +    let xs0 = filter (\v -> degree g v == 0) $ vertices g+        xsn = filter (\v -> degree g v >= (numVertices g) - k + 1) $ vertices g+        g' = foldr (flip removeVertex) g (xsn ++ xs0)+        x1  = take 1 $ filter (\v -> degree g' v == 1) $ vertices g'+    in case x1 of+        [v] ->+          let k0 = length xs0+              g'' = foldr (flip removeVertex) g' $ v : neighbors g' v+              (g''', xs', k') = reduce g'' (k - k0 - 1)+          in (g''', v:xs0 ++ xs', 1 + k0 + k')+        [] -> (g', xs0, length xs0)+          

@@ -0,0 +1,88 @@+module HGraph.Undirected.Solvers.Treedepth+        ( optimalDecomposition+        , treedepthAtMost+        , isDecomposition+        , Decomposition(..)+        )+where++import HGraph.Undirected+import qualified Data.Map as M+import qualified Data.Set as S+import Data.Maybe+import Data.List+import Control.Monad++data Decomposition a = +  Decomposition+  { ancestor :: M.Map a a+  , children :: M.Map a (S.Set a)+  , depth    :: Int+  , roots    :: [a]+  }+  deriving (Eq)++++optimalDecomposition g = fromJust $ foldr mplus Nothing $ map (treedepthAtMost g) [1..]++treedepthAtMost _ 0 = Nothing+treedepthAtMost g k+  | any isNothing ts = Nothing+  | otherwise = Just $ foldl' (\t0 t1 -> +                  Decomposition{ ancestor = M.union (ancestor t0) (ancestor t1)+                               , children = M.union (children t0) (children t1)+                               , depth = max (depth t0) (depth t1)+                               , roots = (roots t1) ++ (roots t0)+                  }) emptyDecomposition+                  $ map fromJust ts+  where+    gs = map (inducedSubgraph g) $ connectedComponents g+    ts = map (\g -> treedepthAtMost' g k) gs++treedepthAtMost' g 0 = Nothing+treedepthAtMost' g 1+  | numVertices g == 1 = Just $ emptyDecomposition { depth = 1, roots = vertices g }+  | otherwise = Nothing+treedepthAtMost' g k = foldr mplus Nothing $ map guess $ vertices g+  where+    guess v = fmap (addRoot v) td+      where+        td = treedepthAtMost (removeVertex g v) (k - 1)++isDecomposition g td =+  all (\(v,u) -> v `S.member` (ancestors M.! u) || u `S.member` (ancestors M.! v)) $+            edges g+  where+    ancestors = M.fromList [ (v, S.fromList $ ancestry v) | v <- vertices g]+    ancestry v+      | isNothing mu = []+      | otherwise = u : ancestry u+      where+        mu = v `M.lookup` (ancestor td) +        Just u = mu++emptyDecomposition = Decomposition { ancestor = M.empty, children = M.empty, roots = [], depth = 0 }++addRoot r td = Decomposition{ ancestor = a' `M.union` ancestor td+                            , children = c' `M.union` children td+                            , depth = 1 + depth td+                            , roots = [r]+                            }+  where+    a' = M.fromList $ zip (roots td) (repeat r)+    c' = M.singleton r  (S.fromList $ roots td)++showTd td = concatMap (showTd' "") (roots td)+  where+    showTd' indent v = indent ++ show v ++ "\n" ++ rs+      where+        mcs = M.lookup v (children td)+        Just cs = mcs+        rs+          | isNothing mcs = ""+          | otherwise = concatMap (showTd' ('-':indent)) (S.toList cs)++instance (Ord a, Show a) => Show (Decomposition a) where+  show = showTd+    

@@ -0,0 +1,56 @@+module HGraph.Undirected.Solvers.VertexCover+        ( minimumVertexCover+        , vertexCoverAtMost+        )+where++import HGraph.Undirected+import Control.Monad+import Data.Maybe+import qualified Data.Map as M+import qualified Data.Set as S++minimumVertexCover :: (Mutable t, UndirectedGraph t, Adjacency t) => t a -> [a]+minimumVertexCover g = map (itol M.!) $ fromJust $ foldr mplus Nothing $ map (vertexCoverAtMost' gi) [1..]+  where+    (gi, assocs) = linearizeVertices g+    itol = M.fromList assocs++vertexCoverAtMost :: (Mutable t, UndirectedGraph t, Adjacency t) => t a -> Int -> Maybe [a]+vertexCoverAtMost g k = fmap (map (itol M.!)) $ vertexCoverAtMost' gi k+  where+    (gi, assocs) = linearizeVertices g+    itol = M.fromList assocs++vertexCoverAtMost' :: (Mutable t, UndirectedGraph t, Adjacency t) => t Int -> Int -> Maybe [Int]+vertexCoverAtMost' g k+  | k < 0 = Nothing+  | k' < 0 = Nothing+  | numEdges g' == 0 = Just sol'+  | numEdges g' > k * k = Nothing+  | otherwise =+    (fmap (v:) $ vertexCoverAtMost' (removeVertex g' v) (k'-1)) `mplus` +    (fmap (nv++) $ vertexCoverAtMost' (foldr (flip removeVertex) g' (v:nv)) (k' - (degree g' v)))+    where+      (g', sol', k') = reduce g k+      e' = edges g'+      (v,_) = head e'+      nv = neighbors g' v++reduce g k = reduce' g k [] (vertices g) S.empty++reduce' g k sol [] _ = (g,sol,k)+reduce' g k sol (v:vs) visited+  | v `S.member` visited = reduce' g k sol vs visited+  | d == 1 = reduce' (removeVertex (removeVertex g v) u) (k-1) (u:sol) (un ++ vs)+                     ( (S.insert v $ S.insert u visited) `S.difference`+                       (S.delete v $ S.fromList un))+  | d == 0 = reduce' (removeVertex g v) k sol vs (S.insert v visited)+  | d > k = reduce' (removeVertex g v) (k - 1) (v:sol) (vn ++ vs)+                    ((S.insert v visited) `S.difference` (S.fromList vn))+  | otherwise = reduce' g k sol vs (S.insert v visited)+  where+    d = degree g v+    u = head $ neighbors g v+    un = neighbors g u+    vn = neighbors g v

@@ -0,0 +1,4 @@+module HGraph.Utils where++mhead []    = Nothing+mhead (x:_) = Just x

@@ -0,0 +1,96 @@+module Main where++import HGraph.Directed+import HGraph.Directed.Connectivity+import qualified HGraph.Directed.AdjacencyMap as AM+import qualified Data.Set as S++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++v1 = 1 :: Int++tests = TestList                         +  [ TestLabel "Maximal paths 1" $ TestCase+    ( do+      let d = addVertex v1 AM.emptyDigraph+          ps = allMaximalPaths d+      assertEqual "Paths"+        [[1]]+        ps+    )+  , TestLabel "Maximal paths 2" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2]) [(1,2)]+          ps = allMaximalPaths d+      assertEqual "Paths"+        [[1,2]]+        ps+    )+  , TestLabel "Maximal paths 3" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4,5]) [(1,2), (2,3), (3,4), (4,5)]+          ps = allMaximalPaths d+      assertEqual "Paths"+        [[1,2,3,4,5]]+        ps+    )+  , TestLabel "Maximal paths 4" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4]) $ zip [1,2,3,4] [2,3,4,1]+          ps = allMaximalPaths d+      assertEqual "Paths"+        (S.fromList $ [ arcSet [1,2,3,4,1]])+        (S.fromList $ map arcSet ps)+    )+  , TestLabel "Maximal paths 5" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4,5]) $ zip [1,2,5,5] [5,5,3,4]+          ps = allMaximalPaths d+      assertEqual "Paths"+        (S.fromList [[1,5,3], [2,5,3], [1,5,4], [2,5,4]])+        (S.fromList ps)+    )+  , TestLabel "Maximal paths 6" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3]) $+                    [ (v,u)+                    | v <- [1..3]+                    , u <- [1..3]+                    , u /= v+                    ]+          ps = allMaximalPaths d+      assertEqual "Paths"+        (S.fromList $ map arcSet +          [ [1,2,1], [1,3,1]+          , [1,2,3,1], [1,3,2,1]+          , [2,3,2]+          ]+        )+        (S.fromList $ map arcSet ps)+    )+  , TestLabel "Maximal paths 7" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2,3,4]) $+                    [ (0,1), (0,2), (0,4)+                    , (1,0), (2,1), (2,4)+                    , (3,1), (3,2), (3,4)+                    , (4,0)+                    ]+          ps = allMaximalPaths d+      assertEqual "Paths"+        (S.fromList $ map arcSet +          [ [3,2,4,0,1], [3,4,0,1]+          , [3,4,0,2,1], [3,1,0,2,4]+          , [3,2,1,0,4], [3,1,0,4]+          ]+        )+        (S.fromList $ map arcSet ps)+    )+  ]++arcSet p = S.fromList $ zip p $ tail p++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,56 @@+module Main where++import HGraph.Directed+import HGraph.Directed.Load+import qualified HGraph.Directed.AdjacencyMap as AM+import qualified Data.Set as S+import Data.Either++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++tests = TestList                         +  [ TestLabel "Digraph 0" $ TestCase+    ( do+      let ed = loadEdgeList AM.emptyDigraph "1 0"+          Right d = ed+      assertBool "Is right"+        (isRight ed)+      assertEqual "Vertices"+        [0]+        (vertices d)+      assertEqual "Arcs"+        []+        (arcs d)+    )+  , TestLabel "Digraph 1" $ TestCase+    ( do+      let ed = loadEdgeList AM.emptyDigraph "2 1 0 1"+          Right d = ed+      assertBool "Is right"+        (isRight ed)+      assertEqual "Vertices"+        [0,1]+        (vertices d)+      assertEqual "Arcs"+        [(0,1)]+        (arcs d)+    )+  , TestLabel "Digraph 2" $ TestCase+    ( do+      let ed = loadEdgeList AM.emptyDigraph "4 2 0 1 1 0"+          Right d = ed+      assertBool "Is right"+        (isRight ed)+      assertEqual "Vertices"+        [0,1,2,3]+        (vertices d)+      assertEqual "Arcs"+        (S.fromList [(0,1), (1,0)])+        (S.fromList $ arcs d)+    )+  ]++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,91 @@+module Main where++import HGraph.Directed+import HGraph.Directed.PathAnonymity+import qualified HGraph.Directed.AdjacencyMap as AM+import qualified Data.Set as S++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++v1 = 1 :: Int++tests = TestList                         +  [ TestLabel "Path anonymity 0" $ TestCase+    ( do+      let d = addVertex v1 AM.emptyDigraph+          k = pathAnonymity d+      assertEqual "Anonymity"+        0+        k+    )+  , TestLabel "Path anonymity 1-0" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2]) $ zip [1] [2]+          k = pathAnonymity d+      assertEqual "Anonymity"+        1+        k+    )+  , TestLabel "Path anonymity 1-1" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2,3,4]) $ zip [0,1,2,4] [4,4,4,3]+          k = pathAnonymity d+      assertEqual "path anonymity"+        1+        (pathPathAnonymityI d [0,4,3])+      assertEqual "digraph anonymity"+        1+        k+    )+  , TestLabel "Path anonymity 2-0" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4,5]) $ zip [1,2,3,3] [3,3,4,5]+          k = pathAnonymity d+      assertEqual "Anonymity"+        2+        k+    )+  , TestLabel "Path anonymity 2-1" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2]) $ zip [0,0,1,1] [1,2,0,2]+          k = pathAnonymity d+      assertEqual "path anonymity"+        2+        (pathPathAnonymityI d [0,1,0])+      assertEqual "digraph anonymity"+        2+        k+    )+  , TestLabel "Path anonymity 4-1" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4,5]) $ [(v,u) | v <- [1..5], u <- [1..5], v /= u]+          k = pathAnonymity d+      assertEqual "path anonymity"+        2+        (pathPathAnonymityI d [1,2,1])+      assertEqual "path anonymity"+        3+        (pathPathAnonymityI d [1,2,3,1])+      assertEqual "digraph anonymity"+        4+        k+    )+  , TestLabel "Path anonymity 5-0" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [v1,2,3,4,5,6]) $ [(v,u) | v <- [1..6], u <- [1..6], v /= u]+          k = pathAnonymity d+      assertEqual "path anonymity"+        5+        (pathPathAnonymityI d [1,2,3,4,5,1])+      assertEqual "digraph anonymity"+        5+        k+    )+  ]++arcSet p = S.fromList $ zip p $ tail p++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,70 @@+module Main where++import HGraph.Directed+import HGraph.Directed.Subgraph+import qualified HGraph.Directed.AdjacencyMap as AM+import qualified Data.Map as M+import qualified Data.Set as S++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++tests = TestList                         +  [ TestLabel "Subgraph 0" $ TestCase+    ( do+      let d = addVertex 1 AM.emptyDigraph+      assertBool "Subgraph"+        (d `contains` d)+    )+  , TestLabel "Subgraph 1" $ TestCase+    ( do+      let d  = foldr addVertex AM.emptyDigraph [0,1]+          h1 = foldr addVertex AM.emptyDigraph [1]+          h2 = foldr addVertex AM.emptyDigraph [2]+      assertBool "Subgraph h1"+        (d `contains` h1)+      assertBool "Subgraph h2"+        (not $ d `contains` h2)+      assertBool "Iso h2"+        (isSubgraphIsomorphism d h2 (M.singleton 2 1))+      assertBool "Subgraph Iso h2"+        (h2 `isSubgraphOf` d)+    )+  , TestLabel "Subgraph 2" $ TestCase+    ( do+      let d = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2,3]) $ zip [0,1,2] [1,2,3]+          h = foldr addArc (foldr addVertex AM.emptyDigraph [0,1]) $ zip [0] [1]+      assertBool "Subgraph h"+        (d `contains` h)+      assertBool "Iso h"+        (isSubgraphIsomorphism d h (M.fromList [(0,0), (1,1)]))+      assertBool "Subgraph Iso h"+        (h `isSubgraphOf` d)+    )+  , TestLabel "Subgraph 3" $ TestCase+    ( do+      let d  = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2,3]) $ zip [0,0,0,1] [1,2,3,0]+          h1 = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2,3,4]) $ []+          h2  = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2]) $ zip [0,0,1] [1,2,0]+      assertBool "not subgraph h"+        (not $ h1 `isSubgraphOf` d)+      assertBool "Subgraph Iso h"+        (h2 `isSubgraphOf` d)+    )+  , TestLabel "Subgraph 4" $ TestCase+    ( do+      let d  = foldr addArc (foldr addVertex AM.emptyDigraph [0,1]) $ zip [0] [1]+          h1 = foldr addArc (foldr addVertex AM.emptyDigraph [0,1]) $ zip [0,1] [1,0]+          h2  = foldr addArc (foldr addVertex AM.emptyDigraph [0,1,2]) $ zip [0,1] [1,2]+      assertBool "subgraph iso h1"+        (d `isSubgraphOf` h1)+      assertBool "Subgraph Iso h2"+        (d `isSubgraphOf` h2)+    )+  ]++arcSet p = S.fromList $ zip p $ tail p++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,33 @@+module Main where++import HGraph.Undirected.AdjacencyMap+import qualified Data.Map as M+import Data.List++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++tests = TestList                         +  [ TestLabel "No edges 1" $ TestCase+    ( do+      let g = addVertex emptyGraph 1+      assertEqual "0" 0 (degree g 1)+      assertEqual "[1]" [[1]] (connectedComponents g)+    )+  , TestLabel "No edges 2" $ TestCase+    ( do+      let g = foldr (flip addVertex) emptyGraph [1,2,3,4,5,6]+      assertEqual "1 2 3 4 5 6" [[1], [2], [3], [4], [5], [6]] (connectedComponents g)+    )+  , TestLabel "Path 1" $ TestCase+    ( do+      let g = addEdge (foldr (flip addVertex) emptyGraph [1,2]) (1,2)+      assertEqual "deg(1) = 1" 1 (degree g 1)+      assertEqual "" [[1,2]] (map sort $ connectedComponents g)+      assertEqual "" [1,2] (sort $ metaBfs g 1 id)+    )+  ]++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,78 @@+module Main where++import HGraph.Undirected.AdjacencyMap+import HGraph.Undirected.Solvers.VertexCover++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++isVc g vc = numEdges (foldr (flip removeVertex) g vc) == 0++tests = TestList                         +  [ TestLabel "No edges 1" $ TestCase+    ( do+      let g = addVertex emptyGraph 1+          vc = minimumVertexCover g+      assertEqual "Empty VC" [] vc+    )+  , TestLabel "No edges 2" $ TestCase+    ( do+      let g = foldr (flip addVertex) emptyGraph [1,2,3,4,5,6]+          vc = minimumVertexCover g+      assertEqual "Empty VC" [] vc+    )+  , TestLabel "VC 1" $ TestCase+    ( do+      let g = addEdge (foldr (flip addVertex) emptyGraph [1,2]) (1,2)+          vc = minimumVertexCover g+      assertEqual "VC = 1" 1 (length vc)+      assertBool  "Is VC" $ isVc g vc+    )+  , TestLabel "VC 2" $ TestCase+    ( do+      let g = foldr (flip addEdge)+                    (foldr (flip addVertex) emptyGraph [1,2,3,4])+                    [(1,2), (1,3), (1,4)]+          vc = minimumVertexCover g+      assertEqual "VC = 1" 1 (length vc)+      assertBool  "Is VC" $ isVc g vc+    )+  , TestLabel "VC 3" $ TestCase+    ( do+      let g = foldr (flip addEdge)+                    (foldr (flip addVertex) emptyGraph [1,2,3,4])+                    [(1,2), (1,3), (1,4), (2,3)]+          vc = minimumVertexCover g+      assertEqual "|VC|" 2 (length vc)+      assertBool  "Is VC" $ isVc g vc+    )+  , TestLabel "VC 4" $ TestCase+    ( do+      let g = foldr (flip addEdge)+                    (foldr (flip addVertex) emptyGraph [1,2,3,4,5,6])+                    ((1,6):(zip [1..5] [2..6]))+          vc = minimumVertexCover g+      assertEqual "|VC|" 3 (length vc)+      assertBool  "Is VC" $ isVc g vc+    )+  , TestLabel "VC grid" $ TestCase+    ( do+      let g = foldr (flip addEdge)+                    (foldr (flip addVertex) emptyGraph [ (x,y) | x <- [1..4], y <- [1..4]])+                    ([((4,y), (4,y+1)) | y <- [1..3]] +++                     [((x,4), (x+1,4)) | x <- [1..3]] +++                     concat [[ ((x,y), (x+1,y))+                             , ((x,y), (x,y+1))+                             ]+                            | x <- [1..3], y <- [1..3]+                            ]+                    )+          vc = minimumVertexCover g+      assertEqual "|VC|" 8 (length vc)+      assertBool  "Is VC" $ isVc g vc+    )+  ]++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess

@@ -0,0 +1,61 @@+module Main where++import HGraph.Undirected.AdjacencyMap+import HGraph.Undirected.Solvers.Treedepth+import qualified Data.Map as M+import Data.List++import Test.HUnit hiding (Node)+import System.Exit (exitFailure, exitSuccess)++tests = TestList                         +  [ TestLabel "No edges 1" $ TestCase+    ( do+      let g = addVertex emptyGraph 1+          td = optimalDecomposition g+      assertEqual "TD"+        Decomposition{ ancestor = M.empty+                     , children = M.empty+                     , roots = [1]+                     , depth = 1+                     }+        td+    )+  , TestLabel "No edges 2" $ TestCase+    ( do+      let g = foldr (flip addVertex) emptyGraph [1,2,3,4,5,6]+          td = optimalDecomposition g+      assertEqual "TD"+        Decomposition{ ancestor = M.empty+                     , children = M.empty+                     , roots = [1,2,3,4,5,6]+                     , depth = 1+                     }+        td{roots = sort $ roots td}+    )+  , TestLabel "Path 1" $ TestCase+    ( do+      let g = addEdge (foldr (flip addVertex) emptyGraph [1,2]) (1,2)+          td = optimalDecomposition g+      assertEqual (show td) 2 (depth td)+      assertBool  (show td) $ isDecomposition g td+    )+  , TestLabel "Path 2" $ TestCase+    ( do+      let g = foldr (flip addEdge) (foldr (flip addVertex) emptyGraph [1,2,3,4,5,6]) [(1,2), (2,3), (3,4), (4,5), (5,6)]+          td = optimalDecomposition g+      assertEqual (show td) 3 (depth td)+      assertBool  (show td) $ isDecomposition g td+    )+  , TestLabel "Cycle 1" $ TestCase+    ( do+      let g = foldr (flip addEdge) (foldr (flip addVertex) emptyGraph [1,2,3,4,5,6]) [(1,2), (2,3), (3,4), (4,5), (5,6), (6,1)]+          td = optimalDecomposition g+      assertEqual (show td) 4 (depth td)+      assertBool  (show td) $ isDecomposition g td+    )+  ]++main = do +  count <- runTestTT tests+  if errors count + failures count > 0 then exitFailure else exitSuccess