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.TH perfect_match 1 "September 1996" "Scilab Group" "Scilab function"
.so ../sci.an
.SH NAME
perfect_match - min-cost perfect matching
.SH CALLING SEQUENCE
.nf
[cst,nmatch] = perfect_match(g,arcost)
.fi
.SH PARAMETERS
.TP 2
g
: graph list
.TP 7
arcost
: integer row vector
.TP 4
cst
: integer
.TP 7
nmatch
: integer row vector
.SH DESCRIPTION
\fVperfect_match\fR finds a perfect min-cost matching for the graph \fVg\fR.
\fVg\fR must be an undirected graph with an even number of nodes.
\fVarcost\fR is the vector of the (integer) costs of the arcs (the dimension
of \fVarcost\fR is twice the number of edges of the graph).
The output is the vector \fVnmatch\fR of the perfect matching and the
corresponding cost \fVcst\fR.
.SH EXAMPLE
.nf
ta=[27 27 3 12 11 12 27 26 26 25 25 24 23 23 21 22 21 20 19 18 18];
ta=[ta 16 15 15 14 12 9 10 6 9 17 8 17 10 20 11 23 23 12 18 28];
he=[ 1 2 2 4 5 11 13 1 25 22 24 22 22 19 13 13 14 16 16 9 16];
he=[he 10 10 11 12 2 6 5 5 7 8 7 9 6 11 4 18 13 3 28 17];
n=28;
g=make_graph('foo',0,n,ta,he);
xx=[46 120 207 286 366 453 543 544 473 387 300 206 136 250 346 408];
g('node_x')=[xx 527 443 306 326 196 139 264 55 58 46 118 513];
yy=[36 34 37 40 38 40 35 102 102 98 93 96 167 172 101 179];
g('node_y')=[yy 198 252 183 148 172 256 259 258 167 109 104 253];
show_graph(g);m2=2*size(ta,2);
arcost=round(100.*rand(1,m2));
[cst,nmatch] = perfect_match(g,arcost);
sp=sparse([ta' he'],[1:size(ta,2)]',[n,n]);
sp1=sparse([[1:n]' nmatch'],ones(1,size(nmatch,2))',[n,n]);
[ij,v,mn]=spget(sp.*sp1);
show_arcs(v');
.fi
.SH SEE ALSO
best_match
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