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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Vydáno v:Mathematical programming Ročník 207; číslo 1-2; s. 717 - 732
Hlavní autoři: Hirayama, Tsuyoshi, Liu, Yuhao, Makino, Kazuhisa, Shi, Ke, Xu, Chao
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer
Témata:
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