Before revision:  Furthermore, our algorithms improve upon the space complexity of ParallelCut . Both of our algorithms have space complexity O(mn^2) whereas ParallelCut has space complexity O(m^2n^2).
After revision:  Furthermore, our algorithms improve upon the space complexity of ParallelCut . Both of our algorithms have space complexity O(mn^2) whereas ParallelCut has space complexity O(m^2n^2).