圖着色算法的實現

Question

我開始知道圖着色算法是NP-Complete問題。不過，我想知道是否可以使用啓發式方法實現任何實現，特別是區別圖着色？如果可能的話，是否有任何合適的資源來了解這一點？

Answer 1

如在稍微related post討論：

約束解算器等MiniZinc能夠解決廣泛的圖着色的問題。

這MiniZinc示例演示Petersen graph的着色：

% Petersen Graph 
set of int: Colors = 1..3; 
set of int: Nodes = 1..10; 
set of int: Edges = 1..15; 
array[Edges] of Nodes: aFrom = [ 1, 2, 3, 4, 1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 6 ]; 
array[Edges] of Nodes: aTo = [ 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 8, 10, 9, 10, 9 ]; 

array[int] of string: colorName = [ "red", "green", "blue", "purple", "yellow", "brown", "black" ]; 

array[Nodes] of var Colors: nodeColor; 

constraint 
    forall(e in Edges) (
     nodeColor[aFrom[e]] != nodeColor[aTo[e]] 
); 

solve satisfy; 

output [ show(colorName[nodeColor[n]]) ++ "\n" | n in Nodes ];