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It is generally believed that the preference ranking method PROMETHEE has aquadratic time complexity. In this paper, however, we present an exactalgorithm that computes PROMETHEE's net flow scores in time O(qn log(n)), whereq represents the number of criteria and n the number of alternatives. Themethod is based on first sorting the alternatives after which the unicriterionflow scores of all alternatives can be computed in one scan over the sortedlist of alternatives while maintaining a sliding window. This method works withthe linear and level criterion preference functions. The algorithm we presentis exact and, due to the sub-quadratic time complexity, vastly extends theapplicability of the PROMETHEE method. Experiments show that with the newalgorithm, PROMETHEE can scale up to millions of tuples.

PROMETHEE is Not Quadratic: An O(qn log(n)) Algorithm