The standard tool for doing this sort of thing in Bioinformatics is the BLAST program. It is used to compare two fragments of molecules (like DNA or proteins) to find where they align with each other - basically where the two strings (sometimes multi GB in size) share common substrings.
The basic algorithm is simple, just systematically break up one of the strings into pieces and compare the pieces with the other string. A simple implementation would be something like:
// Note: not fully tested, there may be bugs:
function subCompare (needle, haystack, min_substring_length) {
// Min substring length is optional, if not given or is 0 default to 1:
min_substring_length = min_substring_length || 1;
// Search possible substrings from largest to smallest:
for (var i=needle.length; i>=min_substring_length; i--) {
for (j=0; j <= (needle.length - i); j++) {
var substring = needle.substr(j,i);
var k = haystack.indexOf(substring);
if (k != -1) {
return {
found : 1,
substring : substring,
needleIndex : j,
haystackIndex : k
}
}
}
}
return {
found : 0
}
}
You can modify this algorithm to do more fancy searches like ignoring case, fuzzy matching the substring, look for multiple substrings etc. This is just the basic idea.