Given a layer assignment and permutation, decide the coordinates for
each vertex. The objective is to encourage straight edges, especially
for longer edges. This function uses an integer program to decide the
coordinates (although it is solved as a linear program), as described in
  Gansner, Emden R., et al.
  A technique for drawing directed graphs.
  Software Engineering, IEEE Transactions on 19.3 (1993): 214-230.
Arguments:
adj_list        Directed graph in adjacency list format
layers          Assignment of vertices
layer_verts     Dictionary of layer => vertices (final perm.)
orig_n          Number of original (non-dummy) vertices
widths          Width of each vertex
xsep            Minimum seperation between each vertex
Returns:
layer_coords    For each layer and vertex, the x-coord

Given a layer assignment, introduce dummy vertices to break up
long edges (more than one layer)
Arguments:
orig_adj_list   Original directed graph in adjacency list format
layers          Assignment of original vertices

Given a layer assignment, decide a permutation for each layer
that attempts to minimizes edge crossings using the barycenter
method proposed in the Sugiyama paper.
Arguments:
adj_list        Directed graph in adjacency list format
layers          Assignment of vertices
layer_verts     Dictionary of layer => vertices

Given a layer assignment, decide a permutation for each layer
that minimizes edge crossings using integer programming.
Based on the IP described in
  M. Junger, E. K. Lee, P. Mutzel, and T. Odenthal.
  A polyhedral approach to the multi-layer crossing minimization problem.
  In G. Di Battista, editor, Graph Drawing: 5th International Symposium,
  GD ’97, volume 1353 of Lecture Notes in Computer Science, pages 13–24,
  Rome, Italy, September 1997. Springer-Verlag.
Arguments:
adj_list        Directed graph in adjacency list format
layers          Assignment of vertices
layer_verts     Dictionary of layer => vertices (initial perm.)
Returns:
new_layer_verts An improved dictionary of layer => vertices (opt. perm.)