An Approximation Algorithm for Random Generation of Capacities

Capacities on a finite set are sets functions vanishing the empty and being monotonic w.r.t. inclusion. Since of capacities is an order polytope, problem randomly generating amounts to all linear extensions Boolean lattice. This known be intractable even as soon $$n>5$$ , therefore approximate methods have been proposed, most notably one based Markov chains. Although quite accurate, this method time consuming. In paper, we propose 2-layer approximation method, which generates subset extensions, eliminating those with very low probability. We show that our has similar performance compared chain but much less