A polynomial time algorithm for finding a minimum 4-partition of a submodular function

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 proble...

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Vydané v:	Mathematical programming Ročník 207; číslo 1-2; s. 717 - 732
Hlavní autori:	Hirayama, Tsuyoshi, Liu, Yuhao, Makino, Kazuhisa, Shi, Ke, Xu, Chao
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024 Springer
Predmet:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical Submodular function 90C27 Combinatorial optimization Polynomial time
ISSN:	0025-5610, 1436-4646
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Popis
Shrnutí:	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.
ISSN:	0025-5610 1436-4646
DOI:	10.1007/s10107-023-02029-0