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yap-6.3/library/wdgraphs.yap
vsc 0dd1ed933e improve graphs a bit. 
git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@2285 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
2008-06-26 13:09:15 +00:00

459 lines
13 KiB
Prolog
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% File : wdgraphs.yap
% Author : Vitor Santos Costa
% Updated: 2006
% Purpose: Weighted Directed Graph Processing Utilities.
:- module( wdgraphs,
[
wdgraph_new/1,
wdgraph_add_edge/5,
wdgraph_add_edges/3,
wdgraph_add_vertices_and_edges/4,
wdgraph_del_edge/5,
wdgraph_del_edges/3,
wdgraph_del_vertex/3,
wdgraph_del_vertices/3,
wdgraph_edge/4,
wdgraph_to_dgraph/2,
dgraph_to_wdgraph/2,
wdgraph_neighbors/3,
wdgraph_neighbours/3,
wdgraph_wneighbors/3,
wdgraph_wneighbours/3,
wdgraph_transpose/2,
wdgraph_transitive_closure/2,
wdgraph_symmetric_closure/2,
wdgraph_top_sort/2,
wdgraph_min_path/5,
wdgraph_min_paths/3,
wdgraph_max_path/5,
wdgraph_path/3,
wdgraph_reachable/3]).
:- reexport(library(dgraphs),
[dgraph_add_vertex/3 as wdgraph_add_vertex,
dgraph_add_vertices/3 as wdgraph_add_vertices,
dgraph_vertices/2 as wdgraph_vertices,
dgraph_edges/2 as wdgraph_edges
]).
:- use_module(library(dgraphs),
[
dgraph_top_sort/2,
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,
rb_clone/4,
rb_update/5,
ord_list_to_rbtree/2]).
:- use_module(library(ordsets),
[ord_insert/3]).
:- use_module(library(heaps),
[
empty_heap/1,
add_to_heap/4,
get_from_heap/4
]).
wdgraph_new(Vertices) :-
rb_new(Vertices).
wdgraph_add_vertices_and_edges(Vs0,Vertices,Edges,Vs2) :-
wdgraph_add_vertices(Vs0, Vertices, Vs1),
wdgraph_add_edges(Vs1, Edges, Vs2).
wdgraph_add_edge(Vs0,V1,V2,Weight,Vs2) :-
wdgraph_new_edge(V1,V2,Weight,Vs0,Vs1),
dgraph_add_vertex(Vs1,V2,Vs2).
wdgraph_add_edges(V0, Edges, VF) :-
rb_empty(V0), !,
sort(Edges,SortedEdges),
all_vertices_in_wedges(SortedEdges,Vertices),
sort(Vertices,SortedVertices),
edges2wgraphl(SortedVertices, SortedEdges, GraphL),
ord_list_to_rbtree(GraphL, VF).
wdgraph_add_edges(G0, Edges, GF) :-
sort(Edges,SortedEdges),
all_vertices_in_wedges(SortedEdges,Vertices),
sort(Vertices,SortedVertices),
add_edges(SortedVertices,SortedEdges, G0, GF).
all_vertices_in_wedges([],[]).
all_vertices_in_wedges([V1-(V2-_)|Edges],[V1,V2|Vertices]) :-
all_vertices_in_wedges(Edges,Vertices).
edges2wgraphl([], [], []).
edges2wgraphl([V|Vertices], [V-(V1-W)|SortedEdges], [V-[V1-W|Children]|GraphL]) :- !,
get_extra_children(SortedEdges,V,Children,RemEdges),
edges2wgraphl(Vertices, RemEdges, GraphL).
edges2wgraphl([V|Vertices], SortedEdges, [V-[]|GraphL]) :-
edges2wgraphl(Vertices, SortedEdges, GraphL).
add_edges([],[]) --> [].
add_edges([VA|Vs],[VB-(V1-W)|Es]) --> { VA == VB }, !,
{ get_extra_children(Es,VA,Children,REs) },
wdgraph_update_vertex(VA,[V1-W|Children]),
add_edges(Vs,REs).
add_edges([V|Vs],Es) --> !,
wdgraph_update_vertex(V,[]),
add_edges(Vs,Es).
get_extra_children([VA-(C-W)|Es],VB,[C-W|Children],REs) :- VA == VB, !,
get_extra_children(Es,VB,Children,REs).
get_extra_children(Es,_,[],Es).
wdgraph_update_vertex(V,Edges,WG0,WGF) :-
rb_update(WG0, V, Edges0, EdgesF, WGF), !,
key_union(Edges, Edges0, EdgesF).
wdgraph_update_vertex(V,Edges,WG0,WGF) :-
rb_insert(WG0, V, Edges, WGF).
key_union([], [], []) :- !.
key_union([], [C|Children], [C|Children]).
key_union([C|Children], [], [C|Children]) :- !.
key_union([K-W|ToAdd], [K1-W1|Children0], NewUnion) :-
( K == K1 ->
NewUnion = [K-W|NewChildren],
key_union(ToAdd, Children0, NewChildren)
;
K1 @< K ->
NewUnion = [K1-W1|NewChildren],
key_union([K-W|ToAdd], Children0, NewChildren)
;
NewUnion = [K-W|NewChildren],
key_union(ToAdd, [K1-W1|Children0], NewChildren)
).
wdgraph_new_edge(V1,V2,W,Vs0,Vs) :-
rb_apply(Vs0, V1, insert_edge(V2,W), Vs), !.
wdgraph_new_edge(V1,V2,W,Vs0,Vs) :-
rb_insert(Vs0,V1,[V2-W],Vs).
insert_edge(V2, W, Children0, Children) :-
ord_insert(Children0,V2-W,Children).
wdgraph_top_sort(WG,Q) :-
wdgraph_to_dgraph(WG, G),
dgraph_top_sort(G, Q).
wgraph_to_wdgraph(UG, DG) :-
ord_list_to_rbtree(UG, DG).
wdgraph_to_wgraph(DG, UG) :-
rb_visit(DG, UG).
wdgraph_edge(N1, N2, W, G) :-
rb_lookup(N1, Ns, G),
find_edge(N2-W, Ns).
find_edge(N-W,[N1-W|_]) :- N == N1, !.
find_edge(El,[_|Edges]) :-
find_edge(El,Edges).
wdgraph_del_edge(Vs0, V1, V2, W, Vs) :-
rb_update(Vs0, V1, Children0, NewChildren, Vs),
del_edge(Children0, V2, W, NewChildren).
% I assume first argument is subset of second.
del_edge([K-W|Children], K1, W1, NewChildren) :-
( K == K1 ->
W = W1,
Children = NewChildren
;
% K1 @< K
NewChildren = [K-W|ChildrenLeft],
del_edge(Children, K1, W1, ChildrenLeft)
).
wdgraph_del_edges(G0, Edges, GF) :-
sort(Edges,SortedEdges),
continue_del_edges(SortedEdges, G0, GF).
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_update(Vs0, V, Children0, NewChildren, Vs),
del_vertices(Children, Children0, NewChildren).
% I assume first argument is subset of second.
del_vertices(Children, [], Children).
del_vertices([K1-W1|Children0], [K-W|ToDel], NewChildren) :-
( K == K1 ->
W = W1,
del_vertices(Children0, ToDel, NewChildren)
;
% K1 @< K
NewChildren = [K1-W1|ChildrenLeft],
del_vertices(Children0, [K-W|ToDel], ChildrenLeft)
).
wdgraph_del_vertex(Vs0, V, Vsf) :-
rb_delete(Vs0, V, Vs1),
rb_map(Vs1, delete_wedge(V), Vsf).
delete_wedge(_, [], []).
delete_wedge(V, [K-W|Children], NewChildren) :-
( K == V ->
NewChildren = Children
;
K @< V ->
NewChildren = [K-W|Children2],
delete_wedge(V, Children, Children2)
;
Children = NewChildren
).
wdgraph_del_vertices(G0, Vs, GF) :-
sort(Vs,SortedVs),
delete_all(SortedVs, G0, G1),
delete_remaining_edges(SortedVs, G1, GF).
% 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_possible_edges(SortedVs), Vsf).
del_possible_edges([], [], []).
del_possible_edges([], [C|Children], [C|Children]).
del_possible_edges([_|_], [], []).
del_possible_edges([K|ToDel], [K1-W1|Children0], NewChildren) :-
( K == K1 ->
del_possible_edges(ToDel, Children0, NewChildren)
;
K1 @< K ->
NewChildren = [K1-W1|ChildrenLeft],
del_possible_edges([K|ToDel], Children0, ChildrenLeft)
;
del_possible_edges(ToDel, [K1-W1|Children0], NewChildren)
).
wdgraph_to_dgraph(WG, DG) :-
rb_clone(WG, EdgesList0, DG, EdgeList),
cvt_wedges(EdgesList0, EdgeList).
cvt_wedges([], []).
cvt_wedges([V-WEs|EdgesList0], [V-Es|EdgesList]) :-
cvt_wneighbs(WEs, Es),
cvt_wedges(EdgesList0, EdgesList).
cvt_wneighbs([], []).
cvt_wneighbs([V-_|WEs], [V|Es]) :-
cvt_wneighbs(WEs, Es).
dgraph_to_wdgraph(DG, WG) :-
rb_clone(DG, EdgesList0, WG, EdgesList),
cvt_edges(EdgesList0, EdgesList).
cvt_edges([], []).
cvt_edges([V-Es|EdgesList0], [V-WEs|WEdgeList]) :-
cvt_neighbs(Es, WEs),
cvt_edges(EdgesList0, WEdgeList).
cvt_neighbs([], []).
cvt_neighbs([V|WEs], [V-1|Es]) :-
cvt_neighbs(WEs, Es).
wdgraph_neighbors(V, WG, Neighbors) :-
rb_lookup(V, EdgesList0, WG),
cvt_wneighbs(EdgesList0, Neighbors).
wdgraph_neighbours(V, WG, Neighbors) :-
rb_lookup(V, EdgesList0, WG),
cvt_wneighbs(EdgesList0, Neighbors).
wdgraph_wneighbors(V, WG, Neighbors) :-
rb_lookup(V, Neighbors, WG).
wdgraph_wneighbours(V, WG, Neighbors) :-
rb_lookup(V, Neighbors, WG).
wdgraph_transpose(Graph, TGraph) :-
rb_visit(Graph, Edges),
rb_clone(Graph, TGraph, NewNodes),
wtedges(Edges,UnsortedTEdges),
sort(UnsortedTEdges,TEdges),
fill_nodes(NewNodes,TEdges).
wtedges([],[]).
wtedges([V-Vs|Edges],TEdges) :-
fill_wtedges(Vs, V, TEdges, TEdges0),
wtedges(Edges,TEdges0).
fill_wtedges([], _, TEdges, TEdges).
fill_wtedges([V1-W|Vs], V, [V1-(V-W)|TEdges], TEdges0) :-
fill_wtedges(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).
wdgraph_transitive_closure(G,Closure) :-
dgraph_edges(G,Edges),
continue_closure(Edges,G,Closure).
continue_closure([], Closure, Closure) :- !.
continue_closure(Edges, G, Closure) :-
transit_wgraph(Edges,G,NewEdges),
wdgraph_add_edges(G, NewEdges, GN),
continue_closure(NewEdges, GN, Closure).
transit_wgraph([],_,[]).
transit_wgraph([V-(V1-W)|Edges],G,NewEdges) :-
rb_lookup(V1, GrandChildren, G),
transit_wgraph2(GrandChildren, V, W, G, NewEdges, MoreEdges),
transit_wgraph(Edges, G, MoreEdges).
transit_wgraph2([], _, _, _, NewEdges, NewEdges).
transit_wgraph2([GC|GrandChildren], V, W, G, NewEdges, MoreEdges) :-
is_edge(V,GC,G), !,
transit_wgraph2(GrandChildren, V, W, G, NewEdges, MoreEdges).
transit_wgraph2([GC-W1|GrandChildren], V, W2, G, [V-(GC-W)|NewEdges], MoreEdges) :-
W is W1+W2,
transit_wgraph2(GrandChildren, V, W2, G, NewEdges, MoreEdges).
is_edge(V1,V2,G) :-
rb_lookup(V1,Children,G),
find_edge(V2-_, Children).
wdgraph_symmetric_closure(G,S) :-
dgraph_edges(G, WEdges),
invert_wedges(WEdges, InvertedWEdges),
wdgraph_add_edges(G, InvertedWEdges, S).
invert_wedges([], []).
invert_wedges([V1-(V2-W)|WEdges], [V2-(V1-W)|InvertedWEdges]) :-
invert_wedges(WEdges, InvertedWEdges).
wdgraph_min_path(V1, V2, WGraph, Path, Cost) :-
rb_new(Status0),
rb_lookup(V1, Edges, WGraph),
rb_insert(Status0, V1, V2, Status),
empty_heap(H0),
queue_edges(Edges, V1, 0, H0, H1),
dijkstra(H1, V2, WGraph, Status, [], EPath),
backtrace(EPath, V2, [V2], Path, 0, Cost).
wdgraph_max_path(V1, V2, WGraph0, Path, Cost) :-
rb_clone(WGraph0, Edges0, WGraph, Edges),
inv_costs(Edges0, Edges),
wdgraph_min_path(V1, V2, WGraph, Path, NCost),
Cost is -NCost.
inv_costs([], []).
inv_costs([V-Es|Edges0], [V-NEs|Edges]) :-
inv_costs2(Es,NEs),
inv_costs(Edges0, Edges).
inv_costs2([],[]).
inv_costs2([V-E|Es],[V-NE|NEs]) :-
NE is -E,
inv_costs2(Es,NEs).
queue_edges([], _, _, H, H).
queue_edges([V-W|Edges], V0, D0, H, NH) :-
D is W+D0,
add_to_heap(H, D, e(V0,V,W), HI),
queue_edges(Edges, V0, D0, HI, NH).
dijkstra(H0, V2, WGraph, Status, Path0, PathF) :-
get_from_heap(H0, D, e(V0, V, W), H1),
continue_dijkstra(H1, V2, WGraph, Status, Path0, PathF, D, V0, V, W).
continue_dijkstra(_, V2, _, _, Path0, [e(V0,V2,W)|Path0], _, V0, V, W) :- V == V2, !.
continue_dijkstra(H1, V2, WGraph, Status, Path0, PathF, _, _, V, _) :-
rb_lookup(V, _, Status), !,
% pick some other node.
dijkstra(H1, V2, WGraph, Status, Path0, PathF).
continue_dijkstra(H1, V2, WGraph, Status0, Path0, PathF, D, V0, V, W) :-
rb_insert(Status0, V, V0, Status),
rb_lookup(V, Edges, WGraph),
queue_edges(Edges, V, D, H1, H2),
dijkstra(H2, V2, WGraph, Status, [e(V0,V,W)|Path0], PathF).
backtrace([], _, Path, Path, Cost, Cost).
backtrace([e(V0,V,C)|EPath], V1, Path0, Path, Cost0, Cost) :-
V == V1, !,
CostI is C+Cost0,
backtrace(EPath, V0, [V0|Path0], Path, CostI, Cost).
backtrace([_|EPath], V1, Path0, Path, Cost0, Cost) :-
backtrace(EPath, V1, Path0, Path, Cost0, Cost).
wdgraph_min_paths(V1, WGraph, T) :-
rb_new(Status0),
rb_lookup(V1, Edges, WGraph),
rb_insert(Status0, V1, V1, Status),
empty_heap(H0),
queue_edges(Edges, V1, 0, H0, H1),
dijkstra(H1, WGraph, Status, [], EPath),
rb_empty(T0),
wdgraph_add_edges(T0, EPath, T).
dijkstra(H0, WGraph, Status, Path0, PathF) :-
get_from_heap(H0, D, e(V0, V, W), H1), !,
continue_dijkstra(H1, WGraph, Status, Path0, PathF, D, V0, V, W).
dijkstra(_, _, _, Path, Path).
continue_dijkstra(H1, WGraph, Status, Path0, PathF, _, _, V, _) :-
rb_lookup(V, _, Status), !,
% pick some other node.
dijkstra(H1, WGraph, Status, Path0, PathF).
continue_dijkstra(H1, WGraph, Status0, Path0, PathF, D, V0, V, W) :-
rb_insert(Status0, V, V0, Status),
rb_lookup(V, Edges, WGraph),
queue_edges(Edges, V, D, H1, H2),
dijkstra(H2, WGraph, Status, [V0-(V-W)|Path0], PathF).
wdgraph_path(V, WG, P) :-
wdgraph_to_dgraph(WG, G),
dgraph_path(V, G, P).
wdgraph_reachable(V, G, Edges) :-
rb_lookup(V, Children, G),
ord_list_to_rbtree([V-[]],Done0),
reachable(Children, Done0, _, G, Edges, []).
reachable([], Done, Done, _, Edges, Edges).
reachable([V-_|Vertices], Done0, DoneF, G, EdgesF, Edges0) :-
rb_lookup(V,_, Done0), !,
reachable(Vertices, Done0, DoneF, G, EdgesF, Edges0).
reachable([V-_|Vertices], Done0, DoneF, G, [V|EdgesF], Edges0) :-
rb_lookup(V, Kids, G),
rb_insert(Done0, V, [], Done1),
reachable(Kids, Done1, DoneI, G, EdgesF, EdgesI),
reachable(Vertices, DoneI, DoneF, G, EdgesI, Edges0).
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