def best_path (o, R, CT, Delta, parms, start_time):
  '''
  Given a set {R} of fillers, returns a tool-path {ph} comprising
  those fillers or their reversals with intervening jumps. Tries to find
  the path with least total execution time, satisfying the constraint
  that no contact in {CT} has a cooling time greater than {Delta}.
  
  This version of the heuristic does not try to generate link traces; it
  always uses a jump to go from one filler to the next. The path will
  start at the point {o}. Uses backtracking with ordered choices.
  '''
  heuristic2_IMP.best_path(R, Delta, parms, start_time)

def best_path_aux(ph, R, Front, Delta, parms, start_time):
  '''
  Given a partial solution {S} for the stroke order optimization
  problem, and the corresponding list of {Front} strokes tries to
  complete it into a full solution {Sfull}. If it succeds returns the
  {Sfull}, the maximum cooling time {Cmax} among the new strokes added,
  and the corresponding side {smax}. If it fails returns None in place
  of {Sfull}. Assumes that the {Front} has at least one stroke in each
  component of the connectivity graph that has not been yet completey
  extruded.
  '''
  heuristic2_IMP.best_path_aux(S, Front, Delta, parms, start_time)