I have a reasonable-sized set of size
N (say 10 000 objects) in which I am searching for groups of compatible elements. Meaning that I have a function
y = f(x_1, x_2, x_3, ..., x_n) returning bool 0/1 answer whether
n elements are compatible. We are interested in executing this search on each subset smaller than 8 elements of
Which is obviously either NP hard or close to this.
Even for pairwise search for
n elements set we have
n^2 pairs to explore, which is somehow doable yet still grows quite fast for big sets.
Yet then it goes nasty when we are looking for triples (identifying 3-element cliques) and quadriple or greater magnitudes.
Would you suggest any machine learning approach to help with this task? Maybe at efficiently sampling the search-space and identifying which subsets to search on, maybe fast heauristic evaluations of the function to direct the searches.