Finding all largest sequences What would be a good / efficient algorithm or approach to find all the largest sequences within a list of chains with varying lengths?
For instance these chains:
0: [4,5,2,1,3,6,8,9]
1: [2,1,3,4,5,6,7,8,10,11]
2: [15,12]

The longest common subsequence would be [2,1,3,6,8] but there is another important subsequence [4,5,6,8] that we would be needed to find.
All other sequences with 2 or more elements would be inside those two chains. For instance [1,3,6] or [5,6,8] or [2,1] are all inside the two resulting chains.
Note: the example uses integers for more clarity but the real data will use floats, and they will be taken as a "match" when both are separate within a given threshold.
 A: This looks like the longest common subsequence problem, solvable with dynamic clustering. It is applied pairwise, to two sequences at a time. If you are interested in generalising this to more than two sequences you will likely need the two-sequence computation as an intermediate step.
See http://en.wikipedia.org/wiki/Longest_common_subsequence_problem
On further reflection, it sounds as if the problem you want to solve is finding all maximal common subsequences between two sequences (i.e. all those that cannot be further extended).
The page referenced above says this:

Indeed the LCS problem is often defined to be finding all common
  subsequences of a     maximum length. This problem inherently has
  higher complexity, as the number of such subsequences is exponential
  in the worst case,[3] even for only two input strings.

It further lists this paper in the references: "A linear space algorithm for computing maximal common subsequences". Communications of the ACM 18 (6): 341–343. doi:10.1145/360825.360861.
I think that the approach that I sketched in the comments will work, and the depth-first search agrees with the possibility of an exponential number of sequences. More importantly, this problem has already been studied and solutions exist. Perhaps use this as the start of a web/literature search.
