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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Bibliographic Details
Published in:Mathematical programming Vol. 207; no. 1-2; pp. 717 - 732
Main Authors: Hirayama, Tsuyoshi, Liu, Yuhao, Makino, Kazuhisa, Shi, Ke, Xu, Chao
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer
Subjects:
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
Online Access:Get full text
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Summary: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