How to use Multiple Paint Components at the same time in java

I'm making a GUI with java which represents the Longest Path Problem I'm using Graphics 2D to draw the vertices and the links between them. I've made a button which calculates the longest path between two vertices I want to make a link that grows slowly so, I've used Thread.sleep() method to make that but when I use it the whole program becomes very slow and lagging. I've Overriden the paintComponent method to draw and I can't use Multi threading because that makes problems with EDT (Event Dispatch Thread). I've saw other topics for Multiple paint Components but nothing helped me.Any ideas or help??

public void paintComponent(Graphics g)
{   
    super.paintComponent(g);
    if(!dragging&&MainFrame.ActiveAddNode)
    g.drawRect(X,Y, 20, 20);//Virtual rectangle for the vertex
    p=new Polygon();
    for(int i=0;i<Node.size();i++)
    {
        p.addPoint(Node.get(i).X+10, Node.get(i).Y+10);
        g.setColor(Node.get(i).c);
        g.fillRect(Node.get(i).X, Node.get(i).Y, 20, 20);//represents the graph vertex
        g.setColor(Color.CYAN);
        g.drawString(""+i, Node.get(i).X+7,  Node.get(i).Y+15);//the number of the vertex

    }
for(int i=0;i<Node.size();i++)
    for(int j=0;j<Node.get(i).Children.size();j++){
        g.setColor(Color.BLUE);
        for(int k=0;k<link.size()-1;k++)
        {
            if(link.get(k)==i&&link.get(k+1)==Node.get(i).Children.get(j)){
                g.setColor(Color.RED);//Highlight the Longest path link
            }
        }

        g.drawLine(Node.get(i).X+10, Node.get(i).Y+10, Node.get(Node.get(i).Children.get(j)).X+10
                ,  Node.get(Node.get(i).Children.get(j)).Y+10);
        int Xsum=(Node.get(i).X+Node.get(Node.get(i).Children.get(j)).X)/2;
        int Ysum=(Node.get(i).Y+Node.get(Node.get(i).Children.get(j)).Y)/2;
        g.drawString(""+Node.get(i).Edges.get(j),Xsum,Ysum);

    }//end of 2nd loop
}//end of paint component

Solution

I've used Thread.sleep()

Don't use Thread.sleep(...) when code is executing on the Event Dispatch Thread (EDT). This will prevent the GUI from painting itself.

The point of the paintComponent(...) method is to paint the current state of the component.

So you need a method(s) that will allow you to dynamically alter the state of the component. So maybe you have a property like: setPathLength(...). So once you calculate the longest path you know how many iterations are required to display the entire path.

Then you need to use a Timer to schedule your animation. Every time the Timer fires you need to increase the "path length" by 1 and then repaint() your component. So each time one more node is painted.

Read the section from the Swing tutorial on How to Use Swing Timers for more information.