kernighan lin算法

这个算法主要用在网络节点的分割。他的思想是将一个网络节点图分割成两个相等的节点集合。为了连接两个社区的边权最小。

step1:随机产生两个节点的集合A和B.

step2:计算A和B中的每个节点的internal cost and external cost

step3:将A中的节点与B中的节点进行交换，计算两个损失权重的差值，也就是原先图的内外权重差，减去转表后的内外权重差。使这个值最后为负为止。

  function Kernighan-Lin(G(V,E)):
       determine a balanced initial partition of the nodes into sets A and B
       A1 := A; B1 := B
       do
          compute D values for all a in A1 and b in B1
          for (n :=  to |V|/)
             find a[i] from A1 and b[j] from B1, such that g[n] = D[a[i]] + D[b[j]] - *c[a[i]][b[j]] is maximal
             move a[i] to B1 and b[j] to A1
             remove a[i] and b[j] from further consideration in this pass
            update D values for the elements of A1 = A1 \ a[i] and B1 = B1 \ b[j]
         end for
         find k which maximizes g_max, the sum of g[],...,g[k]
         if (g_max > ) then
            Exchange a[],a[],...,a[k] with b[],b[],...,b[k]
      until (g_max <= )
   return G(V,E)