Algorithm for drawing a graph structure?

Question

I have a digraph graph G=(V,E) that I would like to redraw because it is currently very messy. This is a flow chart that is being visualized and since |V|>1000 and each v in V has more than 1 outgoing edge, it is very hard to trace by eye. For instance; a node on the lower left corner is connected by an edge to a node on the upper right corner. It would be better, for example, if these two nodes were placed next to each other. There are too many edges and it is a pain to trace each of them.

I have access to and can change the (x,y) coordinates of all the vertices. I would like to redraw G by maintaining it's current structure, in a way that is more human-friendly. I thought that minimizing the number of intersecting edges may be something to start with.

Is there an algorithm that can help me redraw this graph?

My question is, how do I assign (x,y) coordinates to each v in V such that it is organized better and easier to trace and read? How do I express these requirements formally? Should I go with a heuristic, if this is NP? Here is an example for a somewhat organized graph and this is something messy (although much smaller than what I'm dealing with).

Any help will be greatly appreciated. Thanks.

EDIT: I'm still looking for a to-the-point answer. I've researched into planar straight-line and orthogonal drawing methods but what I've got is lengthy research papers. What I'm seeking is an implementation, pseudo-code or at least something to get me started.

EDIT 2: I'm not trying to display the graph. The input to the algorithm shall be the graph G (composed of V and E) and the output shall be {(xi, yi) for each vi in V}

Answer 1

You want to look at graphviz.org; this is a difficult problem on which there has been a lot of research, reimplementing the wheel is not the right way to go.

Probably you'll have to get the java to write out a datafile which a tool like 'dot' can read and use for the graph layout.

Answer 2

That messy one seems to be drawn using spline, try planar straight line algorithm instead. Indeed this is a very difficult problem and I always use GraphViz as my backend graph drawing tools, you can generate that graph you want with -Gsplines=line option.