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Pietro Abate
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160
cycles_functional.ml
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160
cycles_functional.ml
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open Graph
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open ExtLib
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open ExtString
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module G = Pack.Digraph
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module SV = Set.Make(G.V)
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let to_set l = List.fold_right SV.add l SV.empty ;;
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let partition s w = snd(SV.partition (fun e -> e >= w) s);;
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let print_set s =
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String.join " " (List.map (fun e ->
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string_of_int (G.V.label e)
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) (SV.elements s))
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;;
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let extract_subgraph g s =
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let sg = G.create () in
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G.iter_edges (fun v1 v2 ->
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if SV.mem v1 s then G.add_vertex sg v1;
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if SV.mem v2 s then G.add_vertex sg v2;
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if SV.mem v1 s && SV.mem v2 s then
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G.add_edge sg v1 v2
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) g;
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sg
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;;
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let stack_to_list s =
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let l = ref [] in
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Stack.iter (fun e -> l:= e::!l) s;
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!l
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;;
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type block = {
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blocked : (G.V.t,bool) Hashtbl.t;
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notelem : (G.V.t,G.V.t list) Hashtbl.t
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}
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let init_block g =
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let t = {
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blocked = Hashtbl.create 1023;
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notelem = Hashtbl.create 1023;
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} in
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G.iter_vertex (fun node ->
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Hashtbl.add t.blocked node false;
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Hashtbl.add t.notelem node [];
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) g;
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t
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;;
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let get_notelem t n =
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Hashtbl.find t.notelem n
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;;
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let rec unblock t n =
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Printf.eprintf "unblock %d\n" (G.V.label n);
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if Hashtbl.find t.blocked n then begin
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Hashtbl.replace t.blocked n false;
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let l = get_notelem t n in
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List.iter (unblock t) l;
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Hashtbl.replace t.notelem n []
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end
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;;
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let block t n =
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Hashtbl.replace t.blocked n true
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;;
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let is_bloked t n =
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Hashtbl.find t.blocked n
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;;
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let find_all_cycles_johnson g =
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if not G.is_directed then
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assert false;
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(* stack of nodes in current path *)
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let path = Stack.create () in
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let rec circuit t result thisnode startnode component =
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Stack.push thisnode path;
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block t thisnode;
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let (closed,result) =
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G.fold_succ (fun nextnode (c,r) ->
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Printf.eprintf "startnode %d\n" (G.V.label startnode);
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Printf.eprintf "nextnode %d\n" (G.V.label nextnode);
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if G.V.equal nextnode startnode then begin
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Printf.eprintf "closed = true 1\n";
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(true,(Stack.copy path)::r)
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end else begin
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if not(is_bloked t nextnode) then
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circuit t r nextnode startnode component
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else
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(c,r)
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end
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) component thisnode (false,result)
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in
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if closed then begin
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Printf.eprintf "closed = true 3\n";
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unblock t thisnode
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end else
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G.iter_succ (fun nextnode ->
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let l = get_notelem t nextnode in
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if List.mem thisnode l then
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Hashtbl.replace t.notelem nextnode (thisnode::l)
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) component thisnode;
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ignore(Stack.pop path);
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(closed,result)
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in
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(* Johnson's algorithm requires some ordering of the nodes. *)
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let vertex_set = G.fold_vertex SV.add g SV.empty in
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Printf.eprintf "inital vertex set %s\n" (print_set vertex_set);
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SV.fold (fun s result ->
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(* Build the subgraph induced by s and following nodes in the ordering *)
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Printf.eprintf "selected element %d\n" (G.V.label s);
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let subset = SV.add s (partition vertex_set s) in
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Printf.eprintf "subset %s\n" (print_set subset);
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let subgraph = extract_subgraph g subset in
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if G.nb_edges subgraph > 0 then begin
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(* Find the strongly connected component in the subgraph
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* that contains the least node according to the ordering *)
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let scc = G.Components.scc_list subgraph in
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let minnode = SV.min_elt subset in
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Printf.eprintf "minnode %d\n" (G.V.label minnode);
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let mincomp = List.find (fun l -> List.mem minnode l) scc in
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Printf.eprintf "mincomp %s\n" (print_set ((to_set mincomp)));
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(* smallest node in the component according to the ordering *)
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let startnode = minnode in
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let component = extract_subgraph subgraph (to_set mincomp) in
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G.dot_output component (Printf.sprintf "test-component%d.dot" (G.V.label s));
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(* init the block table for this component *)
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let t = init_block component in
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snd(circuit t result startnode startnode component);
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end else begin
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Printf.eprintf "No edges to consider\n";
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result
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end
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) vertex_set []
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;;
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let g = G.Rand.graph ~v:5 ~e:10 () in
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G.dot_output g "test.dot";
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let ll = find_all_cycles_johnson g in
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List.iter (fun path ->
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let path = stack_to_list path in
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Printf.printf "path : %s\n"
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(String.join " " (List.map (fun e -> string_of_int (G.V.label e)) path))
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) ll
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123
cycles_iter.ml
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123
cycles_iter.ml
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@ -0,0 +1,123 @@
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open Graph
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open ExtLib
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open ExtString
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module G = Pack.Digraph
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let find_all_cycles_johnson g =
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if not G.is_directed then
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assert false;
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(* stack of nodes in current path *)
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let path = Stack.create () in
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(* vertex: blocked from search *)
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let blocked = Hashtbl.create 1023 in
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(* graph portions that yield no elementary circuit *)
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let b = Hashtbl.create 1023 in
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(* list to accumulate the circuits found *)
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let result = ref [] in
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let rec circuit thisnode startnode component =
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let stack_to_list s =
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let l = ref [] in
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Stack.iter (fun e -> l:= e::!l) s;
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!l
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in
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let rec unblock thisnode =
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Printf.eprintf "unblock %d\n" (G.V.label thisnode);
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if Hashtbl.find blocked thisnode then begin
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Hashtbl.replace blocked thisnode false;
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List.iter unblock (Hashtbl.find b thisnode);
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Hashtbl.replace b thisnode []
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end
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in
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let closed = ref false in
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Stack.push thisnode path;
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Hashtbl.replace blocked thisnode true;
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G.iter_succ (fun nextnode ->
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Printf.eprintf "startnode %d\n" (G.V.label startnode);
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Printf.eprintf "nextnode %d\n" (G.V.label nextnode);
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if G.V.equal nextnode startnode then begin
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result := ((stack_to_list path))::!result;
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closed := true;
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Printf.eprintf "closed = true 1\n";
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end else begin if not(Hashtbl.find blocked nextnode) then
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if circuit nextnode startnode component then begin
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closed := true;
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Printf.eprintf "closed = true 2\n";
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end
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end
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) component thisnode;
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if !closed then begin
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Printf.eprintf "closed = true 3\n";
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unblock thisnode
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end
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else
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G.iter_succ (fun nextnode ->
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if List.mem thisnode (Hashtbl.find b nextnode) then
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Hashtbl.replace b nextnode (thisnode::(Hashtbl.find b nextnode))
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) component thisnode;
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ignore(Stack.pop path);
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!closed
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in
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let module SV = Set.Make(G.V) in
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let subgraph_ g s =
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let sg = G.create () in
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G.iter_edges (fun v1 v2 ->
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if SV.mem v1 s then G.add_vertex sg v1;
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if SV.mem v2 s then G.add_vertex sg v2;
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if SV.mem v1 s && SV.mem v2 s then
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G.add_edge sg v1 v2
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) g;
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sg
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in
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(* Johnson's algorithm requires some ordering of the nodes.
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* They might not be sortable so we assign an arbitrary ordering.
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*)
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let to_set l = List.fold_right SV.add l SV.empty in
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let vertex_set = G.fold_vertex SV.add g SV.empty in
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let part s w = snd(SV.partition (fun e -> e >= w) s) in
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let print_set s =
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String.join " " (List.map (fun e ->
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string_of_int (G.V.label e)
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) (SV.elements s))
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in
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Printf.eprintf "inital set %s\n" (print_set vertex_set);
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SV.iter (fun s ->
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(* Build the subgraph induced by s and following nodes in the ordering *)
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Printf.eprintf "selected element %d\n" (G.V.label s);
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let subset = SV.add s (part vertex_set s) in
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Printf.eprintf "subset %s\n" (print_set subset);
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let subgraph = subgraph_ g subset in
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if G.nb_edges subgraph > 0 then begin
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let scc = G.Components.scc_list subgraph in
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(* Find the strongly connected component in the subgraph
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* that contains the least node according to the ordering *)
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let minnode = SV.min_elt subset in
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Printf.eprintf "minnode %d\n" (G.V.label minnode);
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let mincomp = List.find (fun l -> List.mem minnode l) scc in
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Printf.eprintf "mincomp %s\n" (print_set ((to_set mincomp)));
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(* smallest node in the component according to the ordering *)
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let startnode = minnode in
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let component = subgraph_ subgraph (to_set mincomp) in
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G.dot_output component (Printf.sprintf "test-component%d.dot" (G.V.label s));
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G.iter_vertex (fun node ->
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Hashtbl.add blocked node false;
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Hashtbl.add b node [];
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) component;
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ignore(circuit startnode startnode component);
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end else
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Printf.eprintf "No edges to consider\n"
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) vertex_set;
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!result
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;;
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let g = G.Rand.graph ~v:5 ~e:10 () in
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G.dot_output g "test.dot";
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let ll = find_all_cycles_johnson g in
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List.iter (fun path ->
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Printf.printf "path : %s\n"
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(String.join " " (List.map (fun e -> string_of_int (G.V.label e)) path))
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) ll
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