A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs

For an edge-weighted graph G with n vertices and m edges, the minimum k-way cut problem is to nd a partition of the vertex set into k non-empty subsets so that the weight sum of edges between di erent subsets is minimized. For this problem with k = 5 and 6, we present a deterministic algorithm that runs in O(n k 2 (nF (n;m)+C 2 (n;m)+n 2 )) = O(mn k log(n 2 =m)) time, where F (n;m) and C 2 (n;m) denote respectively the time bounds required to solve the maximum ow problem and the minimum 2-way cut problem in G. The bounds ~ O(mn 5 ) for k = 5 and ~ O(mn 6 ) for k = 6 improve the previous best randomized bounds ~ O(n 8 ) and ~ O(n 10 ), respectively.