Graph-Matching
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lib/Graph/Matching.pm view on Meta::CPAN
sub max_weight_matching($;$) {
my ($graph, $maxcardinality) = @_;
$maxcardinality = defined($maxcardinality) && $maxcardinality;
#
# Vertices are numbered 0 .. ($nvertex-1).
# Non-trivial blossoms are numbered nvertex .. (2*$nvertex-1)
#
# Edges are numbered 0 .. ($nedge-1).
# Edge endpoints are numbered 0 .. (2*$nedge-1), such that endpoints
# (2*k) and (2*k+1) both belong to the edge with index k.
#
# Many terms used in the comments come from the paper by Galil.
# You will probably need the paper to make sense of this code.
#
# Don't bother with empty graphs.
my $nedge = scalar(@{$graph});
return ( ) if (!$nedge);
lib/Graph/Matching.pm view on Meta::CPAN
if (!defined($nodemap{$_})) {
push @nodelist, $_;
$nodemap{$_} = $#nodelist;
}
}
$maxweight = $wt if ($wt > $maxweight);
$all_integer_weights = $all_integer_weights && ($wt == int($wt));
}
my $nvertex = $#nodelist + 1;
# If $p is an endpoint index,
# $endpoint[$p] is the vertex index to which endpoint $p is attached.
my @endpoint;
$#endpoint = 2*$nedge-1;
for (my $k = $nedge - 1; $k >= 0; $k--) {
$endpoint[2*$k] = $nodemap{$graph->[$k]->[0]};
$endpoint[2*$k+1] = $nodemap{$graph->[$k]->[1]};
}
# If $v is a vertex index,
# $neighbend[$v] refers to an array of remote endpoints attached to $v.
my @neighbend;
$#neighbend = $nvertex-1;
for (my $k = $nedge - 1; $k >= 0; $k--) {
my $v = $endpoint[2*$k];
my $w = $endpoint[2*$k+1];
assert($v != $w);
push @{$neighbend[$v]}, 2*$k + 1;
push @{$neighbend[$w]}, 2*$k;
}
# If $v is a vertex index,
# $mate[$v] is the remote endpoint of its matched edge, or -1 if $v
# is single. (i.e. $endpoint[$mate[$v]] is $v's partner vertex)
# Initially all vertices are single.
my @mate = ( -1 ) x $nvertex;
# If $b is a top-level blossom,
# $label[$b] is 0 if $b is unlabeled (free);
# 1 if $b is an S-vertex/blossom;
# 2 if $b is a T-vertex/blossom.
# The label of a vertex is found by looking at the label of its top-level
# containing blossom.
# If $v is a vertex inside a T-blossom,
# $label[$v] is 2 iff $v is reachable from an S-vertex outside the blossom.
# Labels are assigned during a stage and reset after each augmentation.
my @label = ( 0 ) x (2*$nvertex);
# If $b is a labeled top-level blossom,
# $labelend[$b] is the remote endpoint of the edge through which b obtained
# its label, or -1 if $b's base vertex is single.
# If $v is a vertex inside a T-blossom and $label[$v] == 2,
# $labelend[$v] is the remote endpoint of the edge through which $v is
# reachable from outside the blossom.
my @labelend = ( undef ) x (2*$nvertex);
# If $v is a vertex,
# $inblossom[$v] is the top-level blossom to which $v belongs.
# If $v is a top-level vertex, $v is itself a blossom (a trivial blossom)
# and $inblossom[$v] == $v.
# Initially all vertices are top-level trivial blossoms.
my @inblossom = (0 .. ($nvertex-1));
lib/Graph/Matching.pm view on Meta::CPAN
# If $b is a non-trivial (sub-)blossom,
# $blossomchilds[$b] refers to an ordered array of its sub-blossoms,
# starting with the base and going round the blossom.
my @blossomchilds = ( undef ) x (2*$nvertex);
# If $b is a (sub-)blossom,
# $blossombase[$b] is its base VERTEX (i.e. recursive sub-blossom).\
my @blossombase = ( 0 .. ($nvertex-1), ( undef ) x $nvertex );
# If $b is a non-trivial (sub-)blossom,
# $blossomendps[$b] refers to an array of endpoints on its connecting
# edges, such that $blossomendps[$b]->[$i] is the local endpoint of
# $blossomchilds[$b]->[$i] on the edge that connects it to
# $blossomchilds[$b]->[wrap($i+1)].
my @blossomendps = ( undef ) x (2*$nvertex);
# If $v is a free vertex (or an unreached vertex inside a T-blossom),
# $bestedge[$v] is the remote endpoint on a least-slack edge to an S-vertex
# or -1 if there is no such edge.
# If $b is a (possibly trivial) top-level S-blossom,
# $bestedge[$b] is the remote endpoint on a least-slack edge to a
# different S-blossom, or -1 if there is no such edge.
# This is used for efficient computation of delta2 and delta3.
my @bestedge = ( -1 ) x (2*$nvertex);
# If $b is a non-trivial top-level S-blossom,
# $blossombestedges[$b] refers to an array of remote endpoints on
# least-slack edges to neighbouring S-blossoms, or is undef() if no
# such list has been computed yet.
# This is used for efficient computation of delta3.
my @blossombestedges = ( undef ) x (2*$nvertex);
# List of currently unused blossom numbers.
my @unusedblossoms = ( $nvertex .. (2*$nvertex-1) );
# If $v is a vertex,
# $dualvar[$v] = 2 * u($v) where u($v) is $v's variable in the dual
lib/Graph/Matching.pm view on Meta::CPAN
# be zero.
my @allowedge = ( 0 ) x $nedge;
# Queue of newly discovered S-vertices.
my @queue;
# slack($k)
# returns 2 * slack of edge $k (does not work inside blossoms).
local *slack = sub {
my ($k) = @_;
my $v = $endpoint[2*$k];
my $w = $endpoint[2*$k+1];
my $weight = $graph->[$k]->[2];
return $dualvar[$v] + $dualvar[$w] - 2 * $weight;
};
# blossomleaves($b)
# returns a list of leaf vertices of (sub-)blossom $b.
local *blossomleaves = sub {
my ($b) = @_;
if ($b < $nvertex) {
return @_;
lib/Graph/Matching.pm view on Meta::CPAN
unshift @leaves, @{$blossomchilds[$b]};
}
}
return @leaves;
}
};
# assignlabel($w, $t, $p)
# assigns label $t to the top-level blossom containing vertex $w
# and record the fact that $w was reached through the edge with
# remote endpoint $p.
local *assignlabel = sub {
my ($w, $t, $p) = @_;
DBG("assignlabel($w,$t,$p)") if ($DBG);
my $b = $inblossom[$w];
assert($label[$w] == 0 && $label[$b] == 0);
$label[$w] = $t;
$label[$b] = $t;
$labelend[$w] = $p;
$labelend[$b] = $p;
$bestedge[$w] = -1;
lib/Graph/Matching.pm view on Meta::CPAN
if ($t == 1) {
# $b became an S-blossom; add it(s vertices) to the queue
push @queue, blossomleaves($b);
DBG('PUSH ', join(',', blossomleaves($b))) if ($DBG);
} else {
# $b became a T-blossom; assign label S to its mate.
# (If b is a non-trivial blossom, its base is the only vertex
# with an external mate.)
my $base = $blossombase[$b];
assert($mate[$base] >= 0);
assignlabel($endpoint[$mate[$base]], 1, $mate[$base] ^ 1);
}
};
# scanblossom($v, $w)
# traces back from vertices $v and $w to discover either a new blossom
# or an augmenting path; returns the base vertex of the new blossom or -1.
local *scanblossom = sub {
my ($v, $w) = @_;
DBG("scanblossom($v,$w)") if ($DBG);
# Trace back from $v and $w, placing breadcrumbs as we go.
lib/Graph/Matching.pm view on Meta::CPAN
}
assert($label[$b] == 1);
push @path, $b;
$label[$b] = 5;
# Trace one step back.
assert($labelend[$b] == $mate[$blossombase[$b]]);
if ($labelend[$b] == -1) {
# The base of blossom $b is single; stop tracing this path.
$v = -1;
} else {
$v = $endpoint[$labelend[$b]];
$b = $inblossom[$v];
# $b is a T-blossom; trace one more step back.
assert($label[$b] == 2);
assert($labelend[$b] >= 0);
$v = $endpoint[$labelend[$b]];
}
# Swap v and w so that we alternate between both paths.
if ($w != -1) {
my $t = $v;
$v = $w;
$w = $t;
}
}
# Remove breadcrumbs.
foreach (@path) {
lib/Graph/Matching.pm view on Meta::CPAN
# Return base vertex, if we found one.
return $base;
};
# addblossom($base, $k)
# constructs a new blossom with given base, containing edge $k which
# connects a pair of S vertices; labels the new blossom as S; sets its dual
# variable to zero; relabels its T-vertices to S and adds them to the queue.
local *addblossom = sub {
my ($base, $k) = @_;
my $v = $endpoint[2*$k];
my $w = $endpoint[2*$k+1];
my $bb = $inblossom[$base];
my $bv = $inblossom[$v];
my $bw = $inblossom[$w];
# Create blossom.
my $b = pop(@unusedblossoms);
DBG("addblossom($base,$k) v=$v w=$w -> b=$b") if ($DBG);
$blossombase[$b] = $base;
$blossomparent[$b] = -1;
$blossomparent[$bb] = $b;
# Build lists of sub-blossoms and their interconnecting edge endpoints.
my @path;
my @endps;
# Trace back from $v to $base.
while ($bv != $bb) {
# Add $bv to the new blossom.
$blossomparent[$bv] = $b;
unshift @path, $bv;
unshift @endps, $labelend[$bv];
# Trace one step back.
assert($label[$bv] == 2 || ($label[$bv] == 1 && $labelend[$bv] == $mate[$blossombase[$bv]]));
assert($labelend[$bv] >= 0);
$v = $endpoint[$labelend[$bv]];
$bv = $inblossom[$v];
}
# Add the base sub-blossom;
# add the edge that connects the pair of S vertices.
unshift @path, $bb;
push @endps, (2*$k);
# Trace back from $w to $base.
while ($bw != $bb) {
# Add $bw to the new blossom.
$blossomparent[$bw] = $b;
push @path, $bw;
push @endps, ($labelend[$bw] ^ 1);
# Trace one step back.
assert($label[$bw] == 2 || ($label[$bw] == 1 && $labelend[$bw] == $mate[$blossombase[$bw]]));
assert($labelend[$bw] >= 0);
$w = $endpoint[$labelend[$bw]];
$bw = $inblossom[$w];
}
$blossomchilds[$b] = \@path;
$blossomendps[$b] = \@endps;
# Set new blossom's label to S.
assert($label[$bb] == 1);
$label[$b] = 1;
$labelend[$b] = $labelend[$bb];
# Set dual variable to zero.
$dualvar[$b] = 0;
lib/Graph/Matching.pm view on Meta::CPAN
$inblossom[$v] = $b;
}
# Compute $blossombestedges[$b].
my @bestedgeto = ( -1 ) x (2*$nvertex);
foreach $bv (@path) {
if (!defined($blossombestedges[$bv])) {
# This subblossom does not have a list of least-slack edges;
# get the information from the vertices.
foreach (blossomleaves($bv)) {
foreach my $p (@{$neighbend[$_]}) {
my $j = $endpoint[$p];
my $bj = $inblossom[$j];
if ($bj != $b && $label[$bj] == 1 &&
($bestedgeto[$bj] == -1 ||
slack($p>>1) < slack($bestedgeto[$bj]>>1))) {
$bestedgeto[$bj] = $p;
}
}
}
} else {
# Walk this subblossom's least-slack edges.
foreach my $p (@{$blossombestedges[$bv]}) {
my $j = $endpoint[$p];
my $bj = $inblossom[$j];
if ($bj != $b && $label[$bj] == 1 &&
($bestedgeto[$bj] == -1 ||
slack($p>>1) < slack($bestedgeto[$bj]>>1))) {
$bestedgeto[$bj] = $p;
}
}
}
# Forget about least-slack edges of the subblossom.
$blossombestedges[$bv] = undef;
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$blossombestedges[$b] = \@bestedgeto;
# Select bestedge[b].
$bestedge[$b] = -1;
foreach my $p (@bestedgeto) {
if ($bestedge[$b] == -1 ||
slack($p>>1) < slack($bestedge[$b]>>1)) {
$bestedge[$b] = $p;
}
}
DBG("blossomchilds[$b] = ", join(',', @path)) if ($DBG);
DBG("blossomendps[$b] = ", join('; ', map { $endpoint[$_] . "," . $endpoint[$_^1] } @{$blossomendps[$b]})) if ($DBG);
};
# expandblossom($b, $endstage)
# expands the given top-level blossom.
local *expandblossom = sub {
my ($b, $endstage) = @_;
DBG("expandblossom($b,$endstage) ", join(',', @{$blossomchilds[$b]})) if ($DBG);
# Convert sub-blossoms into top-level blossoms.
foreach my $s (@{$blossomchilds[$b]}) {
$blossomparent[$s] = -1;
lib/Graph/Matching.pm view on Meta::CPAN
}
# If we expand a T-blossom during a stage, its sub-blossoms must be
# relabeled.
if (!$endstage && $label[$b] == 2) {
# Start at the sub-blossom through which the expanding
# blossom obtained its label, and relabel sub-blossoms until
# we reach the base.
# Figure out through which sub-blossom the expanding blossom
# obtained its label initially.
assert($labelend[$b] >= 0);
my $entrychild = $inblossom[$endpoint[$labelend[$b] ^ 1]];
# Decide in which direction we will go round the blossom.
my $j = 0;
my $jstep;
$j++ until ($blossomchilds[$b]->[$j] == $entrychild);
if ($j & 1) {
# Start index is odd; go forward and wrap.
$j -= scalar(@{$blossomchilds[$b]});
$jstep = 1;
} else {
# Start index is even; go backward.
$jstep = -1;
}
# Move along the blossom until we get to the base.
my $p = $labelend[$b];
while ($j != 0) {
# Relabel the T-sub-blossom.
my $q = ($jstep == 1) ? ($blossomendps[$b]->[$j]) :
($blossomendps[$b]->[$j-1]^1);
$label[$endpoint[$p^1]] = 0;
$label[$endpoint[$q^1]] = 0;
assignlabel($endpoint[$p^1], 2, $p);
# Step to the next S-sub-blossom and note its forward endpoint.
$allowedge[$q>>1] = 1;
$j += $jstep;
$p = ($jstep == 1) ? ($blossomendps[$b]->[$j]) :
($blossomendps[$b]->[$j-1]^1);
# Step to the next T-sub-blossom.
$allowedge[$p>>1] = 1;
$j += $jstep;
}
# Relabel the base T-sub-blossom WITHOUT stepping through to
# its mate (so don't call assignlabel).
my $bv = $blossomchilds[$b]->[$j];
$label[$endpoint[$p^1]] = 2;
$label[$bv] = 2;
$labelend[$endpoint[$p^1]] = $p;
$labelend[$bv] = $p;
$bestedge[$bv] = -1;
# Continue along the blossom until we get back to entrychild.
$j += $jstep;
while ($blossomchilds[$b]->[$j] != $entrychild) {
# Examine the vertices of the sub-blossom to see whether
# it is reachable from a neighbouring S-vertex outside the
# expanding blossom.
$bv = $blossomchilds[$b]->[$j];
if ($label[$bv] == 1) {
lib/Graph/Matching.pm view on Meta::CPAN
$v = $_;
last;
}
}
# If the sub-blossom contains a reachable vertex, assign
# label T to the sub-blossom.
if (defined($v)) {
assert($label[$v] == 2);
assert($inblossom[$v] == $bv);
$label[$v] = 0;
$label[$endpoint[$mate[$blossombase[$bv]]]] = 0;
assignlabel($v, 2, $labelend[$v]);
}
$j += $jstep;
}
}
# Recycle the blossom number.
$label[$b] = undef;
$labelend[$b] = undef;
$blossomparent[$b] = undef;
$blossomchilds[$b] = undef;
lib/Graph/Matching.pm view on Meta::CPAN
# Start index is even; go backward.
$jstep = -1;
}
# Move along the blossom until we get to the base.
while ($j != 0) {
# Step to the next sub-blossom and augment it recursively.
$j += $jstep;
$t = $blossomchilds[$b]->[$j];
my $p = ($jstep == 1) ? ($blossomendps[$b]->[$j]) :
($blossomendps[$b]->[$j-1]^1);
augmentblossom($t, $endpoint[$p]) if ($t >= $nvertex);
# Step to the next sub-blossom and augment it recursively.
$j += $jstep;
$t = $blossomchilds[$b]->[$j];
augmentblossom($t, $endpoint[$p^1]) if ($t >= $nvertex);
# Match the edge connecting those sub-blossoms.
$mate[$endpoint[$p]] = $p ^ 1;
$mate[$endpoint[$p^1]] = $p;
DBG("PAIR ", $endpoint[$p], " ", $endpoint[$p^1], " k=", $p>>1) if ($DBG);
}
# Rotate the list of sub-blossoms to put the new base at the front.
my $n = scalar(@{$blossomchilds[$b]});
$blossomchilds[$b] = [ @{$blossomchilds[$b]}[$i .. ($n-1)],
@{$blossomchilds[$b]}[0 .. ($i-1)] ];
$blossomendps[$b] = [ @{$blossomendps[$b]}[$i .. ($n-1)],
@{$blossomendps[$b]}[0 .. ($i-1)] ];
$blossombase[$b] = $blossombase[$blossomchilds[$b]->[0]];
assert($blossombase[$b] == $v);
};
# augmentmatching($k)
# swaps matched/unmatched edges over an alternating path between two
# single vertices; the augmenting path runs through edge $k, which
# connects a pair of S vertices.
local *augmentmatching = sub {
my ($k) = @_;
my $v = $endpoint[2*$k];
my $w = $endpoint[2*$k+1];
DBG("augmentmatching($k) v=$v w=$w") if ($DBG);
DBG("PAIR $v $w k=$k") if ($DBG);
foreach my $p (2*$k+1, 2*$k) {
my $s = $endpoint[$p^1];
# Match vertex s to remote endpoint p. Then trace back from s
# until we find a single vertex, swapping matched and unmatched
# edges as we go.
while (1) {
my $bs = $inblossom[$s];
assert($label[$bs] == 1 &&
$labelend[$bs] == $mate[$blossombase[$bs]]);
# Augment through the S-blossom from s to base.
augmentblossom($bs, $s) if ($bs >= $nvertex);
# Update $mate[$s]
$mate[$s] = $p;
# Trace one step back.
last if ($labelend[$bs] == -1); # stop at single vertex
my $t = $endpoint[$labelend[$bs]];
my $bt = $inblossom[$t];
assert($label[$bt] == 2);
# Trace one step back.
assert($labelend[$bt] >= 0);
$s = $endpoint[$labelend[$bt]];
my $j = $endpoint[$labelend[$bt] ^ 1];
# Augment through the T-blossom from j to base.
assert($blossombase[$bt] == $t);
augmentblossom($bt, $j) if ($bt >= $nvertex);
# Update $mate[$j]
$mate[$j] = $labelend[$bt];
# Keep the opposite endpoint;
# it will be assigned to $mate[$s] in the next step.
$p = $labelend[$bt] ^ 1;
DBG("PAIR $s $t k=", $p>>1) if ($DBG);
}
}
};
# Verify that the optimum solution has been reached.
local *verifyoptimum = sub {
my $vdualoffset = 0;
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# 0. all dual variables are non-negative
foreach (@dualvar[0 .. ($nvertex-1)]) {
assert($_ + $vdualoffset >= 0);
}
foreach (@dualvar[$nvertex .. (2*$nvertex-1)]) {
assert(!defined($_) || $_ >= 0);
}
# 0. all edges have non-negative slack and
# 1. all matched edges have zero slack;
foreach my $k (0 .. ($nedge-1)) {
my $v = $endpoint[2*$k];
my $w = $endpoint[2*$k+1];
my $weight = $graph->[$k]->[2];
my $s = $dualvar[$v] + $dualvar[$w] - 2 * $weight;
my @vblossoms = ( $v );
my @wblossoms = ( $w );
push @vblossoms, $blossomparent[$vblossoms[-1]]
until ($blossomparent[$vblossoms[-1]] == -1);
push @wblossoms, $blossomparent[$wblossoms[-1]]
until ($blossomparent[$wblossoms[-1]] == -1);
while ($#vblossoms >= 0 && $#wblossoms >= 0) {
my $bv = pop(@vblossoms);
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# 2. all single vertices have zero dual value;
foreach my $v (0 .. ($nvertex-1)) {
assert($mate[$v] >= 0 || $dualvar[$v] + $vdualoffset == 0);
}
# 3. all blossoms with positive dual value are full.
foreach my $b ($nvertex .. (2*$nvertex-1)) {
if (defined($blossombase[$b]) && $dualvar[$b] > 0) {
assert((scalar(@{$blossomendps[$b]}) & 1) == 1);
for (my $j = 1; $j <= $#{$blossomendps[$b]}; $j += 2) {
my $p = $blossomendps[$b]->[$j];
assert($mate[$endpoint[$p]] == ($p^1));
assert($mate[$endpoint[$p^1]] == $p);
}
}
}
# Ok.
};
# Check optimized delta2 against a trivial computation.
local *checkdelta2 = sub {
foreach my $v (0 .. ($nvertex-1)) {
if ($label[$inblossom[$v]] == 0) {
my $bd;
foreach my $p (@{$neighbend[$v]}) {
my $w = $endpoint[$p];
if ($label[$inblossom[$w]] == 1) {
my $d = slack($p >> 1);
$bd = $d if (!defined($bd) || $d < $bd);
}
}
assert((!defined($bd) && $bestedge[$v] == -1) || ($bestedge[$v] != -1 && $bd == slack($bestedge[$v]>>1)));
}
}
};
# Check optimized delta3 against a trivial computation.
local *checkdelta3 = sub {
my ($bd, $tbd);
foreach my $b (0 .. (2*$nvertex-1)) {
if (defined($blossomparent[$b]) && $blossomparent[$b] == -1 &&
$label[$b] == 1) {
foreach my $v (blossomleaves($b)) {
foreach my $p (@{$neighbend[$v]}) {
my $w = $endpoint[$p];
if ($inblossom[$w] != $b && $label[$inblossom[$w]] == 1) {
my $d = slack($p>>1);
$bd = $d if (!defined($bd) || $d < $bd);
}
}
}
if ($bestedge[$b] != -1) {
my $w = $endpoint[$bestedge[$b]];
my $v = $endpoint[$bestedge[$b]^1];
assert($inblossom[$v] == $b);
assert($inblossom[$w] != $b);
assert($label[$inblossom[$w]] == 1 && $label[$inblossom[$v]] == 1);
my $d = slack($bestedge[$b]>>1);
$tbd = $d if (!defined($tbd) || $d < $tbd);
}
}
}
assert((!defined($bd) && !defined($tbd)) || ($bd == $tbd));
};
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while (@queue && !$augmented) {
# Take an S vertex from the queue.
my $v = pop(@queue);
DBG("POP v=$v") if ($DBG);
assert($label[$inblossom[$v]] == 1);
# Scan its neighbours:
foreach my $p (@{$neighbend[$v]}) {
# w is a neighbour to v
my $w = $endpoint[$p];
# ignore blossom-internal edges
next if ($inblossom[$v] == $inblossom[$w]);
# check whether edge has zero slack
my $kslack;
if (!$allowedge[$p>>1]) {
$kslack = slack($p>>1);
$allowedge[$p>>1] = ($kslack == 0);
}
if ($allowedge[$p>>1]) {
if ($label[$inblossom[$w]] == 0) {
lib/Graph/Matching.pm view on Meta::CPAN
}
# Take action at the point where minimum delta occurred.
DBG("delta$deltatype=$delta") if ($DBG);
if ($deltatype == 1) {
# No further improvement possible; optimum reached.
last;
} elsif ($deltatype == 2) {
# Use the least-slack edge to continue the search.
$allowedge[$deltaedge>>1] = 1;
my $v = $endpoint[$deltaedge];
assert($label[$inblossom[$v]] == 1);
push @queue, $v;
} elsif ($deltatype == 3) {
# Use the least-slack edge to continue the search.
$allowedge[$deltaedge>>1] = 1;
my $v = $endpoint[$deltaedge];
assert($label[$inblossom[$v]] == 1);
DBG("PUSH $v") if ($DBG);
push @queue, $v;
} elsif ($deltatype == 4) {
# Expand the least-z blossom.
expandblossom($deltablossom, 0);
}
# End of a this substage.
}
lib/Graph/Matching.pm view on Meta::CPAN
}
# Verify that we reached the optimum solution.
verifyoptimum() if ($CHECK_OPTIMUM && $all_integer_weights);
# Return %ret such that $ret[$v] is the vertex to which $v is paired.
my %ret;
for (my $v = 0; $v < $nvertex; $v++) {
if ($mate[$v] != -1) {
assert($endpoint[$mate[$endpoint[$mate[$v]]]] == $v);
$ret{$nodelist[$v]} = $nodelist[$endpoint[$mate[$v]]];
}
}
undef @nodelist;
undef %nodemap;
undef @endpoint;
undef @neighbend;
undef @mate;
undef @label;
undef @labelend;
undef @inblossom;
undef @blossomparent;
undef @blossomchilds;
undef @blossombase;
undef @blossomendps;
( run in 0.657 second using v1.01-cache-2.11-cpan-2b1a40005be )