Algorithm for merging sets that share at least 2 elements

Question

Given a list of sets:

• S_1 : [ 1, 2, 3, 4 ]
• S_2 : [ 3, 4, 5, 6, 7 ]
• S_3 : [ 8, 9, 10, 11 ]
• S_4 : [ 1, 8, 12, 13 ]
• S_5 : [ 6, 7,

Answer 1

Let there be a list of many Sets named (S)

Perform a pass through all elements of S, to determine the range (LOW .. HIGH).

Create an array of pointer to Set, of dimensions (LOW, HIGH), named (M).

do
    Init all elements of M to NULL.   

    Iterate though S, processing them one Set at a time, named (Si).

        Permutate all ordered pairs in Si. (P1, P2) where P1 <= P2.
        For each pair examine M(P1, P2)
            if M(P1, P2) is NULL
                Continue with the next pair.
            otherwise
                Merge Si, into the Set pointed to by, M(P1, P2).
                Remove Si from S, as it has been merged.
                Move on to processing Set S(i + 1)

        If Si was not merged, 
            Permutate again through Si
            For each pair, make M(P1, P2) point to Si.

while At least one set was merged during the pass.

My head is saying this is about Order (2N ln N). Take that with a grain of salt.