Before revision:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest  paths problem, which is solved in time O( min (k|E|, |E|^{3/2})).
After revision:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest paths problem, which is solved in time O( \min (k|E|, |E|^{3/2})).