卡格算法

Question

I'm trying to implement the min-cut Karger's algorithm in Java. For this, I created a Graph class which stores a SortedMap, with an integer index as key and a Vertex object as value, and an ArrayList of Edge objects. Edges stores the index of its incident vertices. Than I merge the vertices of some random edge until the number of vertices reach 2. I repeat this steps a safe number of times. Curiously, in my output I get 2x the number of crossing edges. I mean, if the right answer is 10, after execute n times the algorithm (for n sufficient large), the min of these execution results is 20, what makes me believe the implementation is almost correct. This is the relevant part of code:

    void mergeVertex(int iV, int iW) {

    for (int i = 0; i < edges.size(); i++) {
        Edge e = edges.get(i);
        if (e.contains(iW)) {
            if (e.contains(iV)) {
                edges.remove(i);
                i--;
            } else {
                e.replace(iW, iV);
            }
        }
    }

    vertices.remove(iW);
}

public int kargerContraction(){

    Graph copy = new Graph(this);
    Random r = new Random();
    while(copy.getVertices().size() > 2){
        int i = r.nextInt(copy.getEdges().size());
        Edge e = copy.getEdges().get(i);
        copy.mergeVertex(e.getVertices()[0], e.getVertices()[1]);
    }

    return copy.getEdges().size()/2;
}

Answer 1

Actually the problem was much more simple than I thought. While reading the .txt which contains the graph data, I was counting twice each edge, so logically the minCut returned was 2 times the right minCut.