You don't say how big your arrays are, but once the data is generated, this script takes just over 3/4 of a second to index 1,000,000 items (array_1) and then to process 100,000 items (array_1) against that index; deleting 198 items from the two arrays:

#! perl -slw
use strict;
use Time::HiRes qw[ time ];

our $A //= 1e6;
our $B //= 1e5;

my @alphas = 'aaa'..'zzz';
my @numers = '0'..'9';

print "Gening data...";
my @a = map{ $alphas[ rand @alphas] . $numers[rand @numers] } 1 .. $A;
my @b = map{ $alphas[ rand @alphas] . $numers[rand @numers] } 1 .. $B;
my @c = 1 .. @b;

print "Starting...";
my $start = time;

print "Indexing...";
## index array @a
my %a; undef $a{ $_ } for @a;

print "Removing...";
for my $i ( reverse 0 .. $#b ) {
    exists $a{ $b[ $i ] } and delete $b[$i] and delete $c[$i];
}

printf "Took %.6f seconds to check %d (\@b) against %d (\@a) and remov
+e %d items\n",
    time() - $start, $B, $A, $B - @b

__END__
C:\test>962209 -A=1e6 -B=1e5
Gening data...
Starting...
Indexing...
Removing...
Took 0.771435 seconds to check 100000 (@b) against 1000000 (@a) and re
+move 198 items
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