Description of bipmatch

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bipmatch

PURPOSE

bipmatch --- maximum matching in a bipartite graph

SYNOPSIS

function elist = bipmatch(g,X,Y)

DESCRIPTION

 bipmatch --- maximum matching in a bipartite graph
 This may be called either as bipmatch(g,X,Y) or bipmatch(g,p).
 In either case, g is any graph.
 X,Y are disjoint sets of vertices of g or p is a partition of a subset of
 V(g) into two parts.
 In either case, this returns a maximum matching on the bipartite 
 (sub)graph of G with bipartition (X,Y).

CROSS-REFERENCE INFORMATION

This function calls:

• intersect intersect(g,h1,h2) --- g is set to the intersection of h1 and h2.
• matrix matrix(g) --- return (a copy of) the adjacency matrix of g
• nv nv(g) --- number of vertices in g
• union union(g,h1,h2) --- set g equal to the union of h1 and h2.

This function is called by:

SOURCE CODE

0001 function elist = bipmatch(g,X,Y) 
0002 % bipmatch --- maximum matching in a bipartite graph
0003 % This may be called either as bipmatch(g,X,Y) or bipmatch(g,p).
0004 % In either case, g is any graph.
0005 % X,Y are disjoint sets of vertices of g or p is a partition of a subset of
0006 % V(g) into two parts.
0007 % In either case, this returns a maximum matching on the bipartite
0008 % (sub)graph of G with bipartition (X,Y).
0009 
0010 
0011 if nargin==2
0012     c = parts(X);
0013     if length(c) ~= 2
0014         error('partition must have two parts');
0015     end
0016     X = c{1};
0017     Y = c{2};
0018 else
0019     X = unique(X);
0020     Y = unique(Y);
0021 end
0022 
0023 if length(intersect(X,Y)) > 0
0024     error('The sets X and Y must be disjoint')
0025 end
0026 
0027 n = nv(g);
0028 
0029 Z = union(X,Y);
0030 
0031 if any(Z<1) | any(Z>n)
0032     error('Some vertices out of range')
0033 end
0034 
0035 A = matrix(g);
0036 A = A(X,Y);
0037 
0038 p = dmperm(A); % one of Matlab's best kept secrets :-)
0039 
0040 yidx = find(p);
0041 xidx = p(p>0);
0042 
0043 x = X(xidx);
0044 y = Y(yidx);
0045 
0046 elist = [ x(:), y(:)];
0047 elist = sortrows(elist);

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