typedef map < Tuple<int, 2>, Skyline> Chord_outline_map;
typedef map < Tuple<int, 2>, Box> Column_extent_map;
typedef map <int, Slice> Position_extent_map;
+
class Tie_formatting_problem
{
Chord_outline_map chord_outlines_;
set<int> dot_positions_;
Interval dot_x_;
vector<Tie_specification> specifications_;
+ bool use_horizontal_spacing_;
Tie_configuration_map possibilities_;