The algorithm has important practical application in the layout of digital circuits and components in electronic design automation of VLSI.
[1][2] The input to the algorithm is an undirected graph G = (V, E) with vertex set V, edge set E, and (optionally) numerical weights on the edges in E. The goal of the algorithm is to partition V into two disjoint subsets A and B of equal (or nearly equal) size, in a way that minimizes the sum T of the weights of the subset of edges that cross from A to B.
If the graph is unweighted, then instead the goal is to minimize the number of crossing edges; this is equivalent to assigning weight one to each edge.
The algorithm maintains and improves a partition, in each pass using a greedy algorithm to pair up vertices of A with vertices of B, so that moving the paired vertices from one side of the partition to the other will improve the partition.
After matching the vertices, it then performs a subset of the pairs chosen to have the best overall effect on the solution quality T. Given a graph with n vertices, each pass of the algorithm runs in time O(n2 log n).
Furthermore, let be the difference between the external and internal costs of s. If a and b are interchanged, then the reduction in cost is where
The algorithm attempts to find an optimal series of interchange operations between elements of
and then executes the operations, producing a partition of the graph to A and B.