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(* Test file for Connectivity.sstrong_articulation_points *)
open Graph
module Int = struct
type t = int
let compare = compare
let hash = Hashtbl.hash
let equal = (=)
let default = 0
end
module String = struct
type t = string
let compare = compare
let hash = Hashtbl.hash
let equal = (=)
let default = "X"
end
module GI = Imperative.Digraph.Concrete(Int)
module CI = Components.Connectivity(Builder.I(GI))
module GS = Persistent.Digraph.ConcreteBidirectional(String)
module CS = Components.BiConnectivity(GS)
(* From Fig. 1, Italiano, Laura, and Santaroni, "Finding strong bridges and
strong articulation points in linear time", TCS 447(2012). *)
let g1 = GI.create ()
let () =
GI.add_edge g1 1 2;
GI.add_edge g1 1 3;
GI.add_edge g1 2 3;
GI.add_edge g1 3 1;
GI.add_edge g1 3 4;
GI.add_edge g1 3 6;
GI.add_edge g1 3 7;
GI.add_edge g1 4 5;
GI.add_edge g1 5 1;
GI.add_edge g1 5 2;
GI.add_edge g1 5 4;
GI.add_edge g1 5 7;
GI.add_edge g1 6 5;
GI.add_edge g1 6 7;
GI.add_edge g1 7 6;
GI.add_edge g1 7 5
(* From Fig. 2, Italiano, Laura, and Santaroni, "Finding strong bridges and
strong articulation points in linear time", TCS 447(2012). *)
let g2 = GI.create ()
let () =
GI.add_edge g2 1 2;
GI.add_edge g2 2 3;
GI.add_edge g2 3 4;
GI.add_edge g2 4 5;
GI.add_edge g2 5 6;
GI.add_edge g2 6 1
(* From Fig. 7, Italiano, Laura, and Santaroni, "Finding strong bridges and
strong articulation points in linear time", TCS 447(2012). *)
let g3 =
List.fold_left (fun g (src, dst) -> GS.add_edge g src dst) GS.empty
[("A", "B");
("B", "A");
("B", "E");
("C", "A");
("C", "B");
("C", "D");
("C", "E");
("D", "C");
("D", "E");
("E", "C");
("E", "D");
("E", "J");
("E", "I");
("F", "D");
("F", "J");
("H", "F");
("H", "I");
("I", "H");
("I", "J");
("I", "E");
("J", "E");
("J", "F");
("J", "I") ]
(* From Fig. 3, Jaberi, "On computing the 2-vertex-connected components of
directed graphs", Discrete Applied Mathematicds 204(2016). *)
let g4 = GI.create ()
let () =
GI.add_edge g4 1 2;
GI.add_edge g4 2 3;
GI.add_edge g4 3 5;
GI.add_edge g4 3 9;
GI.add_edge g4 3 11;
GI.add_edge g4 3 12;
GI.add_edge g4 4 1;
GI.add_edge g4 4 5;
GI.add_edge g4 4 7;
GI.add_edge g4 4 9;
GI.add_edge g4 5 3;
GI.add_edge g4 5 4;
GI.add_edge g4 6 7;
GI.add_edge g4 6 9;
GI.add_edge g4 7 6;
GI.add_edge g4 7 8;
GI.add_edge g4 7 9;
GI.add_edge g4 8 6;
GI.add_edge g4 9 3;
GI.add_edge g4 9 4;
GI.add_edge g4 9 6;
GI.add_edge g4 9 7;
GI.add_edge g4 10 3;
GI.add_edge g4 10 11;
GI.add_edge g4 11 10;
GI.add_edge g4 11 12;
GI.add_edge g4 12 3;
GI.add_edge g4 12 10;
GI.add_edge g4 12 13;
GI.add_edge g4 13 14;
GI.add_edge g4 14 3;
GI.add_edge g4 14 10
(* From Fig. 4, Jaberi, "On computing the 2-vertex-connected components of
directed graphs", Discrete Applied Mathematicds 204(2016). *)
let g5 = GI.create ()
let () =
GI.add_edge g5 0 1;
GI.add_edge g5 0 2;
GI.add_edge g5 1 0;
GI.add_edge g5 1 2;
GI.add_edge g5 2 0;
GI.add_edge g5 2 1;
GI.add_edge g5 2 3;
GI.add_edge g5 2 4;
GI.add_edge g5 2 5;
GI.add_edge g5 3 2;
GI.add_edge g5 3 4;
GI.add_edge g5 3 5;
GI.add_edge g5 4 2;
GI.add_edge g5 4 3;
GI.add_edge g5 4 5;
GI.add_edge g5 4 6;
GI.add_edge g5 4 7;
GI.add_edge g5 5 2;
GI.add_edge g5 5 3;
GI.add_edge g5 5 4;
GI.add_edge g5 6 4;
GI.add_edge g5 6 7;
GI.add_edge g5 7 4;
GI.add_edge g5 7 6;
GI.add_edge g5 7 8;
GI.add_edge g5 7 9;
GI.add_edge g5 7 11;
GI.add_edge g5 7 14;
GI.add_edge g5 8 7;
GI.add_edge g5 8 9;
GI.add_edge g5 8 10;
GI.add_edge g5 9 8;
GI.add_edge g5 9 10;
GI.add_edge g5 9 11;
GI.add_edge g5 9 13;
GI.add_edge g5 10 7;
GI.add_edge g5 10 11;
GI.add_edge g5 10 9;
GI.add_edge g5 11 7;
GI.add_edge g5 11 8;
GI.add_edge g5 11 10;
GI.add_edge g5 12 4;
GI.add_edge g5 12 13;
GI.add_edge g5 13 12;
GI.add_edge g5 13 14;
GI.add_edge g5 13 15;
GI.add_edge g5 14 2;
GI.add_edge g5 14 12;
GI.add_edge g5 15 12
let pp_comma p () = Format.(pp_print_char p ','; pp_print_space p ())
let pp_set pp_ele pf s =
Format.(fprintf pf "@[<hv 4>{%a}@]"
(pp_print_list ~pp_sep:pp_comma pp_ele) s)
let () =
let saps1 = CI.sstrong_articulation_points g1 in
let saps2 = CI.sstrong_articulation_points g2 in
let saps3 = CS.sstrong_articulation_points g3 in
let saps4 = CI.sstrong_articulation_points g4 in
let saps5 = CI.sstrong_articulation_points g5 in
Format.(printf "@[<v>%a@,%a@,%a@,%a@,%a@]@."
(pp_set pp_print_int) (CI.S.elements saps1)
(pp_set pp_print_int) (CI.S.elements saps2)
(pp_set pp_print_string) (CS.S.elements saps3)
(pp_set pp_print_int) (CI.S.elements saps4)
(pp_set pp_print_int) (CI.S.elements saps5)
)
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