Maybe for a large file it might be faster with memoize. Or maybe not. Benchmark testing is left up to the user :)

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1138357

use strict;
use warnings;

$_ = <<END;
 PID  PPID  COMMAND
   0     0  sched
   1     0  /sbin/init
   7     0  vmtasks
 105     1  /usr/lib/saf/sac
7184     1  /usr/bin/java
7222     1  /usr/lib/utmpd
7501  6223  /usr/sbin/nscd
7507  7184  /bin/sh
7508  7507  /usr/bin/perl
7510  5044  /usr/bin/grep
7512  4333  /usr/bin/egrep
7515  7508  sh  
7516  7515  <defunct>
8000     1  /second/example/for/testing
8001  8000  <defunct>
END

my (%pids, %memoize);
$pids{$2} = [$3, $1] while /^(\s*(\d+)\s+(\d+).*\n)/gm;

sub trace
  {
  $memoize{$_[0]} //= do
    {   
    my ($ppid, $line) = @{ $pids{shift()} };
    ($ppid ? trace($ppid) : "\n") . $line;
    }   
  }

print trace $_ for /^\s*(\d+)\s+\d+\s+<defunct>/gm;
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