Computing linear rankings from trillions of pairwise outranking situations

We present in this paper a sparse HPC implementation for outranking digraphs of huge orders, up to several millions of decision alternatives. The proposed outranking digraph model is based on a quantiles equivalence class decomposition of the underlying multicriteria performance tableau. When locally ranking each of these ordered components, we may readily obtain an overall linear ranking of big sets of decision alternatives. For the local rankings, both, Copeland's as well as the Net-Flows ranking rules, appear to give the best compromise between, on the one side, the fitness of the overall ranking with respect to the given global outranking relation and, on the other side, computational tractability for very big outranking digraphs modelling up to several trillions of pairwise outranking situations.