Try this:

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11110672
use warnings;
use Algorithm::Diff qw(traverse_sequences);

my %groups;
/\S/ and push @{ $groups{ tr/0-9\n//dr } }, $_ while <DATA>;

for ( values %groups )
  {
  my $summary = shift @$_;
  for ( @$_ )
    {
    my @from = split //, $summary;
    my @to = split //;
    $summary = '';
    traverse_sequences( \@from, \@to,
      {
      MATCH     => sub {$summary .= $from[shift()]},
      DISCARD_A => sub {$summary .= '*'},
      DISCARD_B => sub {$summary .= '*'},
      } );
    $summary =~ tr/*//s;
    }
  print $summary;
  }

__DATA__
a/b/c/p0/m0/b0/r_a_c1_0/q
a/b/c/p0/m0/b0/r_a_c1_1/q
a/b/c/p0/m0/b0/r_a_c1_2/q

some/short/name_2/q
a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q
some/short/name_7/q
a/b/c/p0/m0/d1/r_a_c1_0/q
a/b/c/p0/m0/d1/r_a_c1_999/q
a/b/c/p0/m0/b1/r_a_c1_0/q
a/b/c/p0/m0/b1/r_a_c1_42/q
a/b/c/p0/m0/b1/r_a_c1_2/q
[download]

Outputs:

a/b/c/p0/m0/b*/r_a_c1_*/q
some/short/name_*/q
a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q
a/b/c/p0/m0/d1/r_a_c1_*/q
[download]