longest common consecutive subsequence

Question

I know how to find the lcs of two sequences/strings, but lcs doesn't impose a restriction that the subsequence needs to be consecutive. I've tried it as follows

function lccs(a, b)
    if a.length == 0 or b.length == 0
        return ""
    possible = []
    if a[0] == b[0]
      possible.push(lcs(a[1:), b[1:])
    possible.push(lcs(a[1:], b))
    possible.push(lcs(a, b[1:))
    return longest_string(possible)

where longest_string returns the longest string in an array, and s[1:] means a slice of s, starting from the first character.

I've run this both inside a browser in javascript, and in golang, on a remote server where I put each call to lccs in its own goroutine, although I have no idea about the server's hardware specs, so I have no idea of the parallelization of these routines.

In both these cases, in ran way too slowly for my needs. Is there a way to speed this up?

Answer 1

I believe that the basic idea would be to use dynamic programming. something like that:

for i in 1:length(a) {
    for j in 1:length(b) {
        if (a[i]==b[j]) then {
            result[i,j] = result[i-1,j-1]+1 #remember to initialize the borders with zeros
            # track the maximum of the matrix
        } else {
            result[i,j]=0
        }
    }
}

this question is basically similra to the context of sequence alignment, common in bioinformatics. in fact, you should be able to use existing sequence alignment algorithms for your purpose (such as blast, etc.) by setting the "gap" penalties to very high values, practically disallowing gaps in the alignment