performance tuning - Combining lists with common elements efficiently

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Computing the equivalence classes of the symmetric transitive closure of a relation

I am required to process sets consisting of 2-element subsets of integers by combining those subsets whose intersection is nonempty.

For example, given

X = {{1, 2}, {3, 4}, {7, 4}, {2, 5}}

my routine merge will output

merge[X] = {{3, 4, 7}, {1, 2, 5}} .

As all List elements are considered as sets, duplicate entries and list order are to be ignored.

In fact I have implemented such an algorithm in Mathematica, however I suspect it is horribly inefficient and am looking for any reasonable way to improve its performance.

My implementation uses FixedPoint and is broken into two parts :

merge0[x_] := Block[{x0 = x},
Do[
If[i != j && Intersection[x[[i]], x[[j]]] != {}, 
x0 = Join[Delete[x, {{i}, {j}}], {Union@Flatten[Join[x[[i]], x[[j]]]]}];
Break[]], 
{i, Length[x]}, {j, i}]; x0]


merge[x_] := FixedPoint[merge0, x]

Thanks and regards,

Daniel

Comments

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