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yap-6.3/library/undgraphs.yap

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/**
* @file undgraphs.yap
* @author VITOR SANTOS COSTA <vsc@VITORs-MBP.lan>
* @date 2006
*
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* @brief Undirected Graph Processing Utilities.
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*
*
*/
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:- module( undgraphs,
[
undgraph_add_edge/4,
undgraph_add_edges/3,
undgraph_add_vertices/3,
undgraph_del_edge/4,
undgraph_del_edges/3,
undgraph_del_vertex/3,
undgraph_del_vertices/3,
undgraph_edges/2,
undgraph_neighbors/3,
undgraph_neighbours/3,
undgraph_components/2,
undgraph_min_tree/2]).
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/** @defgroup undgraphs Undirected Graphs
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@ingroup library
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@{
The following graph manipulation routines use the red-black tree graph
library to implement undirected graphs. Mostly, this is done by having
two directed edges per undirected edge.
*/
:- reexport( library(dgraphs),
[
dgraph_new/1 as undgraph_new,
dgraph_add_vertex/3 as undgraph_add_vertex,
dgraph_vertices/2 as undgraph_vertices,
dgraph_complement/2 as undgraph_complement,
dgraph_symmetric_closure/2 as dgraph_to_undgraph,
dgraph_edge/3 as undgraph_edge,
dgraph_reachable/3 as undgraph_reachable
]).
:- use_module( library(dgraphs),
[
dgraph_add_edge/4,
dgraph_add_edges/3,
dgraph_add_vertices/3,
dgraph_del_edge/4,
dgraph_del_edges/3,
dgraph_del_vertex/3,
dgraph_del_vertices/3,
dgraph_edges/2,
dgraph_neighbors/3,
dgraph_neighbours/3]).
:- use_module(library(wundgraphs), [
undgraph_to_wundgraph/2,
wundgraph_min_tree/3,
wundgraph_max_tree/3,
wundgraph_to_undgraph/2]).
:- use_module(library(ordsets),
[ ord_del_element/3,
ord_union/3,
ord_subtract/3]).
:- use_module(library(rbtrees),
[ rb_delete/4,
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rb_delete/3,
rb_insert/4,
rb_in/3,
rb_partial_map/4
]).
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/**
@pred undgraph_new(+ _Graph_)
Create a new directed graph. This operation must be performed before
trying to use the graph.
*/
/** @pred undgraph_complement(+ _Graph_, - _NewGraph_)
Unify _NewGraph_ with the graph complementary to _Graph_.
*/
/** @pred undgraph_vertices(+ _Graph_, - _Vertices_)
Unify _Vertices_ with all vertices appearing in graph
_Graph_.
*/
undgraph_add_edge(Vs0,V1,V2,Vs2) :-
dgraphs:dgraph_new_edge(V1,V2,Vs0,Vs1),
dgraphs:dgraph_new_edge(V2,V1,Vs1,Vs2).
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/** @pred undgraph_add_edges(+ _Graph_, + _Edges_, - _NewGraph_)
Unify _NewGraph_ with a new graph obtained by adding the list of
edges _Edges_ to the graph _Graph_.
*/
undgraph_add_edges(G0, Edges, GF) :-
dup_edges(Edges, DupEdges),
dgraph_add_edges(G0, DupEdges, GF).
dup_edges([],[]).
dup_edges([E1-E2|Edges], [E1-E2,E2-E1|DupEdges]) :-
dup_edges(Edges, DupEdges).
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/** @pred undgraph_add_vertices(+ _Graph_, + _Vertices_, - _NewGraph_)
Unify _NewGraph_ with a new graph obtained by adding the list of
vertices _Vertices_ to the graph _Graph_.
*/
undgraph_add_vertices(G, [], G).
undgraph_add_vertices(G0, [V|Vs], GF) :-
dgraph_add_vertex(G0, V, GI),
undgraph_add_vertices(GI, Vs, GF).
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/** @pred undgraph_edges(+ _Graph_, - _Edges_)
Unify _Edges_ with all edges appearing in graph
_Graph_.
*/
undgraph_edges(Vs,Edges) :-
dgraph_edges(Vs,DupEdges),
remove_dups(DupEdges,Edges).
remove_dups([],[]).
remove_dups([V1-V2|DupEdges],NEdges) :- V1 @< V2, !,
NEdges = [V1-V2|Edges],
remove_dups(DupEdges,Edges).
remove_dups([_|DupEdges],Edges) :-
remove_dups(DupEdges,Edges).
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/** @pred undgraph_neighbours(+ _Vertex_, + _Graph_, - _Vertices_)
Unify _Vertices_ with the list of neighbours of vertex _Vertex_
in _Graph_.
*/
undgraph_neighbours(V,Vertices,Children) :-
dgraph_neighbours(V,Vertices,Children0),
(
ord_del_element(Children0,V,Children)
->
true
;
Children = Children0
).
undgraph_neighbors(V,Vertices,Children) :-
dgraph_neighbors(V,Vertices,Children0),
(
ord_del_element(Children0,V,Children)
->
true
;
Children = Children0
).
undgraph_del_edge(Vs0,V1,V2,VsF) :-
dgraph_del_edge(Vs0,V1,V2,Vs1),
dgraph_del_edge(Vs1,V2,V1,VsF).
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/** @pred undgraph_del_edges(+ _Graph_, + _Edges_, - _NewGraph_)
Unify _NewGraph_ with a new graph obtained by removing the list of
edges _Edges_ from the graph _Graph_. Notice that no vertices
are deleted.
*/
undgraph_del_edges(G0, Edges, GF) :-
dup_edges(Edges,DupEdges),
dgraph_del_edges(G0, DupEdges, GF).
undgraph_del_vertex(Vs0, V, Vsf) :-
rb_delete(Vs0, V, BackEdges, Vsi),
(
ord_del_element(BackEdges,V,RealBackEdges)
->
true
;
BackEdges = RealBackEdges
),
rb_partial_map(Vsi, RealBackEdges, del_edge(V), Vsf).
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/** @pred undgraph_del_vertices(+ _Graph_, + _Vertices_, - _NewGraph_)
Unify _NewGraph_ with a new graph obtained by deleting the list of
vertices _Vertices_ and all the edges that start from or go to a
vertex in _Vertices_ to the graph _Graph_.
*/
undgraph_del_vertices(G0, Vs, GF) :-
sort(Vs,SortedVs),
delete_all(SortedVs, [], BackEdges, G0, GI),
ord_subtract(BackEdges, SortedVs, TrueBackEdges),
delete_remaining_edges(SortedVs, TrueBackEdges, GI, 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([], BackEdges, BackEdges) --> [].
delete_all([V|Vs], BackEdges0, BackEdgesF, Vs0,Vsf) :-
rb_delete(Vs0, V, NewEdges, Vsi),
ord_union(NewEdges,BackEdges0,BackEdgesI),
delete_all(Vs, BackEdgesI ,BackEdgesF, Vsi,Vsf).
delete_remaining_edges(SortedVs, TrueBackEdges, Vs0,Vsf) :-
rb_partial_map(Vs0, TrueBackEdges, del_edges(SortedVs), Vsf).
del_edges(ToRemove,E0,E) :-
ord_subtract(E0,ToRemove,E).
del_edge(ToRemove,E0,E) :-
ord_del_element(E0,ToRemove,E).
undgraph_min_tree(G, T) :-
undgraph_to_wundgraph(G, WG),
wundgraph_min_tree(WG, WT, _),
wundgraph_to_undgraph(WT, T).
undgraph_max_tree(G, T) :-
undgraph_to_wundgraph(G, WG),
wundgraph_max_tree(WG, WT, _),
wundgraph_to_undgraph(WT, T).
undgraph_components(Graph,[Map|Gs]) :-
pick_node(Graph,Node,Children,Graph1), !,
undgraph_new(Map0),
rb_insert(Map0, Node, Children, Map1),
expand_component(Children, Map1, Map, Graph1, NGraph),
undgraph_components(NGraph,Gs).
undgraph_components(_,[]).
expand_component([], Map, Map, Graph, Graph).
expand_component([C|Children], Map1, Map, Graph1, NGraph) :-
rb_delete(Graph1, C, Edges, Graph2), !,
rb_insert(Map1, C, Edges, Map2),
expand_component(Children, Map2, Map3, Graph2, Graph3),
expand_component(Edges, Map3, Map, Graph3, NGraph).
expand_component([_|Children], Map1, Map, Graph1, NGraph) :-
expand_component(Children, Map1, Map, Graph1, NGraph).
pick_node(Graph,Node,Children,Graph1) :-
rb_in(Node,Children,Graph), !,
rb_delete(Graph, Node, Graph1).
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%% @}