feat(encode): add vertex cover encoding

src/Sift/Encode/VertexCover.hs

@@ -0,0 +1,29 @@
+module Sift.Encode.VertexCover
+  ( vertexCover
+  , decodeVertexCover
+  , validVertexCover
+  ) where
+
+import Sift.Types
+import Sift.Encode.Cardinality (atMostK)
+import Sift.Encode.Coloring (Graph(..))
+import qualified Data.Map.Strict as Map
+
+vertexCover :: Int -> Graph -> CNF
+vertexCover k (Graph vertices edges) = CNF (edgeClauses ++ cardClauses)
+  where
+    inCover v = posLit (Var v)
+    edgeClauses = [ [inCover u, inCover w] | (u, w) <- edges ]
+    (cardClauses, _) = atMostK k [ inCover v | v <- [1 .. vertices] ] (vertices + 1)
+
+decodeVertexCover :: Int -> Assignment -> [Int]
+decodeVertexCover vertices asn =
+  [ v | v <- [1 .. vertices], Map.findWithDefault False (Var v) asn ]
+
+validVertexCover :: Int -> Graph -> Assignment -> Bool
+validVertexCover k (Graph vertices edges) asn =
+  length cover <= k
+    && all (\(u, w) -> u `elem` coverSet || w `elem` coverSet) edges
+  where
+    cover = decodeVertexCover vertices asn
+    coverSet = cover