Attempt 3:

#! perl -slw
use strict;
use Algorithm::Combinatorics qw[ combinations ];

my $favourite = 1009;
my $n = <>;
my %pairings;
push( @{ $pairings{ $_->[0] } }, $_->[1] ),
push( @{ $pairings{ $_->[1] } }, $_->[0] ),
    while @{ $_ = [split ' ', <> ] };

my @ids = keys %pairings;

my %idPos; @idPos{ @ids } = 0 .. @ids;
my %posId; @posId{ values %idPos } = keys %idPos;

my @masks;
for my $id ( @ids ) {
    $masks[ $idPos{ $id } ] = '';
    vec( $masks[ $idPos{ $id } ], $idPos{ $id }, 1 ) = 1;
    vec( $masks[ $idPos{ $id } ], $idPos{ $_  }, 1 ) = 1
        for @{ $pairings{ $id } };
}

my @hits;
for my $k ( 1 .. $n ) {
    my $iter = combinations( [0 .. $#ids], $k );
    while( my $c = $iter->next ) {
        my $ored = '';
        $ored |= $masks[ $_ ] for @$c;
        my $count = unpack '%32b*', $ored;
        push @hits, [ $k, @$c ] if $count >= @ids;
    }
    last if @hits;
}

if( @hits > 1 ) {
    @hits = sort{ $a->[0] <=> $b->[0] } @hits;
    my $min = $hits[0][0];
    my $i = $#hits;
    --$i while $hits[ $i ][0] > $min;
    $#hits = $i;
    if( @hits > 1 ) {
        my $first = $hits[ 0 ];
        @hits = grep {
            scalar grep{
                $posId{ $_ } == $favourite;
            } @$_[ 0 .. $#{ $_ } ];
        } @hits;
        @hits = @hits >= 1 ? $hits[ 0 ] : $first;
    }
}

print @{ $hits[0] } -1;
print $posId{ $_ } for @{ $hits[0] }[ 1 .. $#{ $hits[ 0 ] } ];
[download]

A run:

C:\test>Bilateral2.pl
20
1001 2000
1002 2000
1009 2000
1011 2010
1012 2010
1013 2010
1021 2020
1022 2020
1023 2020
1031 2030
1032 2030
1033 2030
1041 2040
1042 2040
1043 2040
1100 2000
1100 2010
1100 2020
1100 2030
1100 2040
^Z
5
2020
2030
2000
2010
2040
[download]

Actual:


> Bilateral2.pl
7
71 34
71 1001
72 1002
73 1003
1001 2000
1002 2000
1003 2000
^D
3
1002
71
1003
[download]


Expected:


4
1001
1002
1003
71 or 34
[download]

Sorry, but I think you are wrong here and that my actual solution is correct.

     / 1001 - 71 - 34
2000 - 1002 - 72
     \ 1003 - 73
[download]

If you have 1003, you don't need 73 or 2000.

If you have 1002, you don't need 72 (or 2000).

If you have 71, you don't need 34 or 1001.

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

Nice example!

You're right, thanks. Rewriting...