A provably asymptotically fast version of the generalized jensen algorithm for non-dominated sorting

Abstract

The non-dominated sorting algorithm by Jensen, generalized by Fortin et al to handle the cases of equal objective values, has the running time complexity of O(N logK−1 N) in the general case. Here N is the number of points, K is the number of objectives and K is thought to be a constant when N varies. However, the complexity was not proven to be the same in the worst case. A slightly modified version of the algorithm is presented, for which it is proven that its worst-case running time complexity is O(N logK−1 N).