The difference between a substring and a subsequence is that a subsequence is not necessarily contiguous (all the characters must be present, and in the correct order, but there can be unrelated characters in between).
In that case, I think the easiest way to search for subsequences in Perl is to use regular expressions. For example, if the subsequence is "abcd", then the regular expression to look for a subsequence is /a.*?b.*?c.*?d/.

And since you can easily contruct a regex out of a string, that is easy toconstruct: 

$string = 'abcd';
$regex = join '.*?', split //, $string;
$sequence = 'xxxxxaxxxxxxbxxxxxcxxxxdxxxxx';
if($sequence =~ /$regex/s) {
    printf "I found a match, at offset %d and with total length %d\n",
+ $-[0], $+[0]-$-[0];
}

[download]
Result:
I found a match, at offset 5 and with total length 19

In reply to Re^2: Can KMP be used to find the longest common subsequence? by bart
in thread Can KMP be used to find the longest common subsequence? by Anonymous Monk

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