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。

 1  function Kernighan-Lin(G(V,E)):
 2      determine a balanced initial partition of the nodes into sets A and B
 3      A1 := A; B1 := B
 4      do
 5         compute D values for all a in A1 and b in B1
 6         for (n := 1 to |V|/2)
 7            find a[i] from A1 and b[j] from B1, such that g[n] = D[a[i]] + D[b[j]] - 2*c[a[i]][b[j]] is maximal
 8            move a[i] to B1 and b[j] to A1
 9            remove a[i] and b[j] from further consideration in this pass
 10           update D values for the elements of A1 = A1  a[i] and B1 = B1  b[j]
 11        end for
 12        find k which maximizes g_max, the sum of g[1],...,g[k]
 13        if (g_max > 0) then
 14           Exchange a[1],a[2],...,a[k] with b[1],b[2],...,b[k]
 15     until (g_max <= 0)
 16  return G(V,E)