% File : dgraphs.yap % Author : Vitor Santos Costa % Updated: 2006 % Purpose: Directed Graph Processing Utilities. :- module( dgraphs, [ dgraph_new/1, dgraph_add_edge/4, dgraph_add_edges/3, dgraph_add_vertex/3, dgraph_add_vertices/3, dgraph_del_edge/4, dgraph_del_edges/3, dgraph_del_vertex/3, dgraph_del_vertices/3, dgraph_edge/3, dgraph_edges/2, dgraph_vertices/2, dgraph_to_ugraph/2, ugraph_to_dgraph/2, dgraph_neighbors/3, dgraph_neighbours/3, dgraph_complement/2, dgraph_transpose/2, dgraph_compose/3, dgraph_transitive_closure/2, dgraph_symmetric_closure/2, dgraph_top_sort/2, dgraph_top_sort/3, dgraph_min_path/5, dgraph_max_path/5, dgraph_min_paths/3, dgraph_isomorphic/4, dgraph_path/3]). :- use_module(library(rbtrees), [rb_new/1, rb_empty/1, rb_lookup/3, rb_apply/4, rb_insert/4, rb_visit/2, rb_keys/2, rb_delete/3, rb_map/3, rb_clone/3, ord_list_to_rbtree/2]). :- use_module(library(ordsets), [ord_insert/3, ord_union/3, ord_subtract/3, ord_del_element/3, ord_memberchk/2]). :- use_module(library(wdgraphs), [dgraph_to_wdgraph/2, wdgraph_min_path/5, wdgraph_max_path/5, wdgraph_min_paths/3]). dgraph_new(Vertices) :- rb_new(Vertices). dgraph_add_edge(V1,V2,Vs0,Vs2) :- dgraph_new_edge(V1,V2,Vs0,Vs1), dgraph_add_vertex(V2,Vs1,Vs2). dgraph_add_edges(Edges, V0, VF) :- rb_empty(V0), !, sort(Edges,SortedEdges), all_vertices_in_edges(SortedEdges,Vertices), sort(Vertices,SortedVertices), edges2graphl(SortedVertices, SortedEdges, GraphL), ord_list_to_rbtree(GraphL, VF). dgraph_add_edges(Edges) --> { sort(Edges,SortedEdges), all_vertices_in_edges(SortedEdges,Vertices), sort(Vertices,SortedVertices) }, dgraph_add_edges(SortedVertices,SortedEdges). all_vertices_in_edges([],[]). all_vertices_in_edges([V1-V2|Edges],[V1,V2|Vertices]) :- all_vertices_in_edges(Edges,Vertices). edges2graphl([], [], []). edges2graphl([V|Vertices], [VV-V1|SortedEdges], [V-[V1|Children]|GraphL]) :- V == VV, !, get_extra_children(SortedEdges,VV,Children,RemEdges), edges2graphl(Vertices, RemEdges, GraphL). edges2graphl([V|Vertices], SortedEdges, [V-[]|GraphL]) :- edges2graphl(Vertices, SortedEdges, GraphL). dgraph_add_edges([],[]) --> []. dgraph_add_edges([V|Vs],[V0-V1|Es]) --> { V == V0 }, !, { get_extra_children(Es,V,Children,REs) }, dgraph_update_vertex(V,[V1|Children]), dgraph_add_edges(Vs,REs). dgraph_add_edges([V|Vs],Es) --> !, dgraph_update_vertex(V,[]), dgraph_add_edges(Vs,Es). get_extra_children([V-C|Es],VV,[C|Children],REs) :- V == VV, !, get_extra_children(Es,VV,Children,REs). get_extra_children(Es,_,[],Es). dgraph_update_vertex(V,Children, Vs0, Vs) :- rb_apply(Vs0, V, add_edges(Children), Vs), !. dgraph_update_vertex(V,Children, Vs0, Vs) :- rb_insert(Vs0,V,Children,Vs). add_edges(E0,E1,E) :- ord_union(E0,E1,E). dgraph_new_edge(V1,V2,Vs0,Vs) :- rb_apply(Vs0, V1, insert_edge(V2), Vs), !. dgraph_new_edge(V1,V2,Vs0,Vs) :- rb_insert(Vs0,V1,[V2],Vs). insert_edge(V2, Children0, Children) :- ord_insert(Children0,V2,Children). dgraph_add_vertices([]) --> []. dgraph_add_vertices([V|Vs]) --> dgraph_add_vertex(V), dgraph_add_vertices(Vs). dgraph_add_vertex(V,Vs0,Vs0) :- rb_lookup(V,_,Vs0), !. dgraph_add_vertex(V, Vs0, Vs) :- rb_insert(Vs0, V, [], Vs). dgraph_edges(Vs,Edges) :- rb_visit(Vs,L0), cvt2edges(L0,Edges). dgraph_vertices(Vs,Vertices) :- rb_keys(Vs,Vertices). cvt2edges([],[]). cvt2edges([V-Children|L0],Edges) :- children2edges(Children,V,Edges,Edges0), cvt2edges(L0,Edges0). children2edges([],_,Edges,Edges). children2edges([Child|L0],V,[V-Child|EdgesF],Edges0) :- children2edges(L0,V,EdgesF,Edges0). dgraph_neighbours(V,Vertices,Children) :- rb_lookup(V,Children,Vertices). dgraph_neighbors(V,Vertices,Children) :- rb_lookup(V,Children,Vertices). add_vertices(Graph, [], Graph). add_vertices(Graph, [V|Vertices], NewGraph) :- rb_insert(Graph, V, [], IntGraph), add_vertices(IntGraph, Vertices, NewGraph). dgraph_complement(Vs0,VsF) :- dgraph_vertices(Vs0,Vertices), rb_map(Vs0,complement(Vertices),VsF). complement(Vs,Children,NewChildren) :- ord_subtract(Vs,Children,NewChildren). dgraph_del_edge(V1,V2,Vs0,Vs1) :- rb_apply(Vs0, V1, delete_edge(V2), Vs1). dgraph_del_edges(Edges) --> { sort(Edges,SortedEdges) }, continue_del_edges(SortedEdges). continue_del_edges([]) --> []. continue_del_edges([V-V1|Es]) --> !, { get_extra_children(Es,V,Children,REs) }, contract_vertex(V,[V1|Children]), continue_del_edges(REs). contract_vertex(V,Children, Vs0, Vs) :- rb_apply(Vs0, V, del_edges(Children), Vs). del_edges(ToRemove,E0,E) :- ord_subtract(E0,ToRemove,E). dgraph_del_vertex(V,Vs0,Vsf) :- rb_delete(Vs0, V, Vs1), rb_map(Vs1, delete_edge(V), Vsf). delete_edge(V, Edges0, Edges) :- ord_del_element(Edges0, V, Edges). dgraph_del_vertices(Vs) --> { sort(Vs,SortedVs) }, delete_all(SortedVs), delete_remaining_edges(SortedVs). % it would be nice to be able to delete a set of elements from an RB tree % but I don't how to do it yet. delete_all([]) --> []. delete_all([V|Vs],Vs0,Vsf) :- rb_delete(Vs0, V, Vsi), delete_all(Vs,Vsi,Vsf). delete_remaining_edges(SortedVs,Vs0,Vsf) :- rb_map(Vs0, del_edges(SortedVs), Vsf). dgraph_transpose(Graph, TGraph) :- rb_visit(Graph, Edges), rb_clone(Graph, TGraph, NewNodes), tedges(Edges,UnsortedTEdges), sort(UnsortedTEdges,TEdges), fill_nodes(NewNodes,TEdges). tedges([],[]). tedges([V-Vs|Edges],TEdges) :- fill_tedges(Vs, V, TEdges, TEdges0), tedges(Edges,TEdges0). fill_tedges([], _, TEdges, TEdges). fill_tedges([V1|Vs], V, [V1-V|TEdges], TEdges0) :- fill_tedges(Vs, V, TEdges, TEdges0). fill_nodes([],[]). fill_nodes([V-[Child|MoreChildren]|Nodes],[V-Child|Edges]) :- !, get_extra_children(Edges,V,MoreChildren,REdges), fill_nodes(Nodes,REdges). fill_nodes([_-[]|Edges],TEdges) :- fill_nodes(Edges,TEdges). dgraph_compose(T1,T2,CT) :- rb_visit(T1,Nodes), compose(Nodes,T2,NewNodes), dgraph_new(CT0), dgraph_add_edges(NewNodes,CT0,CT). compose([],_,[]). compose([V-Children|Nodes],T2,NewNodes) :- compose2(Children,V,T2,NewNodes,NewNodes0), compose(Nodes,T2,NewNodes0). compose2([],_,_,NewNodes,NewNodes). compose2([C|Children],V,T2,NewNodes,NewNodes0) :- rb_lookup(C, GrandChildren, T2), compose3(GrandChildren, V, NewNodes,NewNodesI), compose2(Children,V,T2,NewNodesI,NewNodes0). compose3([], _, NewNodes, NewNodes). compose3([GC|GrandChildren], V, [V-GC|NewNodes], NewNodes0) :- compose3(GrandChildren, V, NewNodes, NewNodes0). dgraph_transitive_closure(G,Closure) :- dgraph_edges(G,Edges), continue_closure(Edges,G,Closure). continue_closure([], Closure, Closure) :- !. continue_closure(Edges, G, Closure) :- transit_graph(Edges,G,NewEdges), dgraph_add_edges(NewEdges, G, GN), continue_closure(NewEdges, GN, Closure). transit_graph([],_,[]). transit_graph([V-V1|Edges],G,NewEdges) :- rb_lookup(V1, GrandChildren, G), transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges), transit_graph(Edges, G, MoreEdges). transit_graph2([], _, _, NewEdges, NewEdges). transit_graph2([GC|GrandChildren], V, G, NewEdges, MoreEdges) :- is_edge(V,GC,G), !, transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges). transit_graph2([GC|GrandChildren], V, G, [V-GC|NewEdges], MoreEdges) :- transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges). is_edge(V1,V2,G) :- rb_lookup(V1,Children,G), ord_memberchk(V2, Children). dgraph_symmetric_closure(G,S) :- dgraph_edges(G, Edges), invert_edges(Edges, InvertedEdges), dgraph_add_edges(InvertedEdges, G, S). invert_edges([], []). invert_edges([V1-V2|Edges], [V2-V1|InvertedEdges]) :- invert_edges(Edges, InvertedEdges). dgraph_top_sort(G, Q) :- dgraph_top_sort(G, Q, []). dgraph_top_sort(G, Q, RQ0) :- % O(E) rb_visit(G, Vs), % O(E) invert_and_link(Vs, Links, UnsortedInvertedEdges, AllVs, Q), % O(V) rb_clone(G, LinkedG, Links), % O(Elog(E)) sort(UnsortedInvertedEdges, InvertedEdges), % O(E) dgraph_vertices(G, AllVs), start_queue(AllVs, InvertedEdges, Q, RQ), continue_queue(Q, LinkedG, RQ, RQ0). invert_and_link([], [], [], [], []). invert_and_link([V-Vs|Edges], [V-NVs|ExtraEdges], UnsortedInvertedEdges, [V|AllVs],[_|Q]) :- inv_links(Vs, NVs, V, UnsortedInvertedEdges, UnsortedInvertedEdges0), invert_and_link(Edges, ExtraEdges, UnsortedInvertedEdges0, AllVs, Q). inv_links([],[],_,UnsortedInvertedEdges,UnsortedInvertedEdges). inv_links([V2|Vs],[l(V2,A,B,S,E)|VLnks],V1,[V2-e(A,B,S,E)|UnsortedInvertedEdges],UnsortedInvertedEdges0) :- inv_links(Vs,VLnks,V1,UnsortedInvertedEdges,UnsortedInvertedEdges0). dup([], []). dup([_|AllVs], [_|Q]) :- dup(AllVs, Q). start_queue([], [], RQ, RQ). start_queue([V|AllVs], [VV-e(S,B,S,E)|InvertedEdges], Q, RQ) :- V == VV, !, link_edges(InvertedEdges, VV, B, S, E, RemainingEdges), start_queue(AllVs, RemainingEdges, Q, RQ). start_queue([V|AllVs], InvertedEdges, [V|Q], RQ) :- start_queue(AllVs, InvertedEdges, Q, RQ). link_edges([V-e(A,B,S,E)|InvertedEdges], VV, A, S, E, RemEdges) :- V == VV, !, link_edges(InvertedEdges, VV, B, S, E, RemEdges). link_edges(RemEdges, _, A, _, A, RemEdges). continue_queue([], _, RQ0, RQ0). continue_queue([V|Q], LinkedG, RQ, RQ0) :- rb_lookup(V, Links, LinkedG), close_links(Links, RQ, RQI), % not clear whether I should deleted V from LinkedG continue_queue(Q, LinkedG, RQI, RQ0). close_links([], RQ, RQ). close_links([l(V,A,A,S,E)|Links], RQ, RQ0) :- ( S == E -> RQ = [V| RQ1] ; RQ = RQ1), close_links(Links, RQ1, RQ0). ugraph_to_dgraph(UG, DG) :- ord_list_to_rbtree(UG, DG). dgraph_to_ugraph(DG, UG) :- rb_visit(DG, UG). dgraph_edge(N1, N2, G) :- rb_lookup(N1, Ns, G), ord_memberchk(N2, Ns). dgraph_min_path(V1, V2, Graph, Path, Cost) :- dgraph_to_wdgraph(Graph, WGraph), wdgraph_min_path(V1, V2, WGraph, Path, Cost). dgraph_max_path(V1, V2, Graph, Path, Cost) :- dgraph_to_wdgraph(Graph, WGraph), wdgraph_max_path(V1, V2, WGraph, Path, Cost). dgraph_min_paths(V1, Graph, Paths) :- dgraph_to_wdgraph(Graph, WGraph), wdgraph_min_path(V1, WGraph, Paths). dgraph_path(V, G, [V|P]) :- rb_lookup(V, Children, G), ord_del_element(Children, V, Ch), do_path(Ch, G, [V], P). do_path([], _, _, []). do_path([C|Children], G, SoFar, Path) :- do_children([C|Children], G, SoFar, Path). do_children([V|_], G, SoFar, [V|Path]) :- rb_lookup(V, Children, G), ord_subtract(Children, SoFar, Ch), ord_insert(SoFar, V, NextSoFar), do_path(Ch, G, NextSoFar, Path). do_children([_|Children], G, SoFar, Path) :- do_children(Children, G, SoFar, Path). dgraph_isomorphic(Vs, Vs2, G1, G2) :- rb_new(Map0), mapping(Vs,Vs2,Map0,Map), dgraph_edges(G1,Edges), translate_edges(Edges,Map,TEdges), dgraph_new(G20), dgraph_add_vertices(Vs2,G20,G21), dgraph_add_edges(TEdges,G21,G2). mapping([],[],Map,Map). mapping([V1|Vs],[V2|Vs2],Map0,Map) :- rb_insert(Map0,V1,V2,MapI), mapping(Vs,Vs2,MapI,Map). translate_edges([],_,[]). translate_edges([V1-V2|Edges],Map,[NV1-NV2|TEdges]) :- rb_lookup(V1,NV1,Map), rb_lookup(V2,NV2,Map), translate_edges(Edges,Map,TEdges).