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use strict;
use warnings;
...
        editDistance($shortLeft,  $shortRight)  #replace
    );
}

$ time perl editDistance.pl
11 <LMIjkHFSAE:dmqkdjfERZG>
...
real    2m29.329s
user    1m2.578s
sys     1m26.452s

$ time perl editDistance.pl
11 <LMIjkHFSAE:dmqkdjfERZG>
...
real    0m0.075s
user    0m0.015s
sys     0m0.030s

use strict;
use warnings;
...

memoize("editDistance");
editDistance(...);