1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
|
.TH min_weight_tree 1 "September 1995" "Scilab Group" "Scilab function"
.so ../sci.an
.SH NAME
min_weight_tree - minimum weight spanning tree
.SH CALLING SEQUENCE
.nf
t = min_weight_tree([i],g)
.fi
.SH PARAMETERS
.TP 2
i
: integer, node number of the root of the tree
.TP 2
g
: graph list
.TP 2
t
: row vector of integer numbers of the arcs of the tree if it exists
.SH DESCRIPTION
\fVmin_weight_tree\fR tries to find a minimum weight spanning tree for the
graph \fVg\fR. The optional argument \fVi\fR is the number of the root node of
the tree; its default value is node number 1. This node is meaningless
for an undirected graph.
The weights are given by the element \fVedge_weight\fR of the graph list.
If its value is not given (empty vector \fV[]\fR), it is assumed to be
equal to 0 on each edge.
Weigths can be positive, equal to 0 or negative. To compute a spanning
tree without dealing with weights, give to weights a value of 0 on each
edge or the empty vector \fV[]\fR.
\fVmin_weight_tree\fR returns the tree \fVt\fR as a row vector of the
arc numbers (directed graph) or edge numbers (undirected graph)
if it exists or the empty vector \fV[]\fR otherwise.
If the tree exists, the dimension of \fVt\fR is the number of nodes less 1.
If \fVt(i)\fR is the root of the tree:
- for j < i, \fVt(j)\fR is the number of the arc in the tree after
node \fVt(j)\fR
- for j > i, \fVt(j)\fR is the number of the arc in the tree before
node \fVt(j)\fR
.SH EXAMPLE
.nf
ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 10 10 10 11 12 13 13 13 14 15 16 16 17 17];
he=[2 10 3 5 7 4 2 4 6 8 6 9 7 7 11 15 12 13 9 10 14 11 16 1 17 14 15];
g=make_graph('foo',1,17,ta,he);
g('node_x')=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642];
g('node_y')=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301];
show_graph(g);
t=min_weight_tree(1,g);
g1=g; ma=arc_number(g1); n=g1('node_number');
nodetype=0*ones(1,n); nodetype(1)=2; g1('node_type')=nodetype;
edgecolor=1*ones(1,ma); edgecolor(t)=11*ones(t); g1('edge_color')=edgecolor;
edgewidth=1*ones(1,ma); edgewidth(t)=4*ones(t); g1('edge_width')=edgewidth;
x_message('Minimum weight tree from node 1');
show_graph(g1);
.fi
|
