diff --git a/Data/Algorithm/MaximalCliques.hs b/Data/Algorithm/MaximalCliques.hs new file mode 100644 --- /dev/null +++ b/Data/Algorithm/MaximalCliques.hs @@ -0,0 +1,42 @@ +{- | +Module : Data.Algorithm.MaximalCliques +Copyright : (c) Gershom Bazerman, 2010 +License : BSD 3 Clause +Maintainer : gershomb@gmail.com +Stability : experimental + +This library uses the Bron-Kerbosch algorithm to enumerate all maximal cliques in an undirected graph. A clique is a set of nodes such that there is an edge between every node and every other node in the set. A maximal clique is a clique such that no node may be added while preserving the clique property. + +Maximal clique enumeration is ExpTime complete, and even finding the greatest single clique (the maximum clique) is NP-complete. The Bron-Kerbosch algorithm is known to run well in practice while maintaining a simple implementation. If more efficiency is desired, there are now better algorithms. See, for example, Makino and Uno: . Patches providing improved implementations are more than welcome. + +-} +module Data.Algorithm.MaximalCliques where + +import Data.List (mapAccumL) +import qualified Data.IntSet as S +import qualified Data.Vector as V + +-- | Given a list of nodes, and a function that determines whether there is an edge between any two nodes, yields a list of maximal cliques -- sets of nodes such that every node is connected to every other, and such that no other node may be added while maintaining this property. +getMaximalCliques :: (a -> a -> Bool) -> [a] -> [[a]] +getMaximalCliques tolFun xs = map (map (fst . (V.!) lv) . S.toList) $ + maximalCliques pickpivot (snd . ((V.!) lv)) (S.fromList $ map fst lnodes) + where lnodes = zip [0..] xs + lnodes' = map (\(k,n) -> (n,S.fromList $ filter (/=k) $ map fst $ filter (tolFun n . snd) lnodes)) lnodes + lv = V.fromList lnodes' + pickpivot p x = head $ S.elems p ++ S.elems x + +-- | The Bron-Kerbosch algorithm for finding all maximal cliques in an undirected graph. +-- . Works on nodes represented as 'Int's. +maximalCliques :: (S.IntSet -> S.IntSet -> Int) -- ^ A function that given two 'IntSet's, chooses a member of one as a pivot. + -> (Int -> S.IntSet) -- ^ A function that given a node id, yields the set of its neighbors. + -> S.IntSet -- ^ The set of all nodes in the graph. + -> [S.IntSet] -- ^ An enumeration of all maximal cliques in the graph. +maximalCliques pickpivot neighborsOf nodeset = go S.empty nodeset S.empty + where go r p x + | S.null p && S.null x = [r] + | otherwise = + let pivot = pickpivot p x + step' (p',x') v = + let nv = neighborsOf v + in ((S.delete v p', S.insert v x'), go (S.insert v r) (S.intersection nv p') (S.intersection nv x')) + in concat . snd $ mapAccumL step' (p,x) $ S.elems (p S.\\ neighborsOf pivot) diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,30 @@ +Copyright (c)2010, Gershom Bazerman + +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + * Redistributions in binary form must reproduce the above + copyright notice, this list of conditions and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + * Neither the name of Gershom Bazerman nor the names of other + contributors may be used to endorse or promote products derived + from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/maximal-cliques.cabal b/maximal-cliques.cabal new file mode 100644 --- /dev/null +++ b/maximal-cliques.cabal @@ -0,0 +1,60 @@ +-- maximal-cliques.cabal auto-generated by cabal init. For additional +-- options, see +-- http://www.haskell.org/cabal/release/cabal-latest/doc/users-guide/authors.html#pkg-descr. +-- The name of the package. +Name: maximal-cliques + +-- The package version. See the Haskell package versioning policy +-- (http://www.haskell.org/haskellwiki/Package_versioning_policy) for +-- standards guiding when and how versions should be incremented. +Version: 0.1 + +-- A short (one-line) description of the package. +Synopsis: Enumerate all maximal cliques of a graph. + +-- A longer description of the package. +Description: Enumerate all maximal cliques of a graph. A clique is a set of nodes such that there is an edge between every node and every other node in the set. A maximal clique is a clique such that no node may be added while preserving the clique property. + +-- The license under which the package is released. +License: BSD3 + +-- The file containing the license text. +License-file: LICENSE + +-- The package author(s). +Author: Gershom Bazerman + +-- An email address to which users can send suggestions, bug reports, +-- and patches. +Maintainer: gershomb@gmail.com + +-- A copyright notice. +-- Copyright: + +Category: Algorithms + +Build-type: Simple + +-- Extra files to be distributed with the package, such as examples or +-- a README. +-- Extra-source-files: + +-- Constraint on the version of Cabal needed to build this package. +Cabal-version: >=1.2 + + +Library + -- Modules exported by the library. + Exposed-modules: Data.Algorithm.MaximalCliques + + -- Packages needed in order to build this package. + Build-depends: base > 3, base < 5, containers, vector + + ghc-options: -Wall + + -- Modules not exported by this package. + -- Other-modules: + + -- Extra tools (e.g. alex, hsc2hs, ...) needed to build the source. + -- Build-tools: +