A polynomial time algorithm for finding a minimum 4-partition of a submodular function - Hirayama, Tsuyoshi; Liu, Yuhao; Makino, Kazuhisa; Shi, Ke; Xu, Chao (Mathematical programming, 2024)
In this paper, we study the minimum k -partition problem of submodular functions, i.e., given a finite set V and a submodular function f : 2 V → R , computing a k -partition { V 1 , … , V k } of V with minimum ∑ i = 1 k f ( V i ) . The problem is a natural generalization of the minimum k -cut problem in graphs and hypergraphs. It is known that the problem is NP-hard for general k , and solvable in polynomial time for fixed k ≤ 3 . In this paper, we construct the first polynomial-time algorithm for the minimum 4-partition problem.