Size-constrained submodular minimization through minimum norm base

Kiyohito Nagano, Yoshinobu Kawahara, Kazuyuki Aihara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Citations (Scopus)

Abstract

A number of combinatorial optimization problems in machine learning can be described as the problem of minimizing a submodular function. It is known that the unconstrained submodular minimization problem can be solved in strongly polynomial time. However, additional constraints make the problem intractable in many settings. In this paper, we discuss the submodular minimization under a size constraint, which is NP-hard, and generalizes the densest subgraph problem and the uniform graph partitioning problem. Because of NP-hardness, it is difficult to compute an optimal solution even for a prescribed size constraint. In our approach, we do not give approximation algorithms. Instead, the proposed algorithm computes optimal solutions for some of possible size constraints in polynomial time. Our algorithm utilizes the basic polyhedral theory associated with submodular functions. Additionally, we evaluate the performance of the proposed algorithm through computational experiments.

Original languageEnglish
Title of host publicationProceedings of the 28th International Conference on Machine Learning, ICML 2011
Pages977-984
Number of pages8
Publication statusPublished - Oct 7 2011
Externally publishedYes
Event28th International Conference on Machine Learning, ICML 2011 - Bellevue, WA, United States
Duration: Jun 28 2011Jul 2 2011

Publication series

NameProceedings of the 28th International Conference on Machine Learning, ICML 2011

Conference

Conference28th International Conference on Machine Learning, ICML 2011
CountryUnited States
CityBellevue, WA
Period6/28/117/2/11

Fingerprint

Polynomials
Combinatorial optimization
Approximation algorithms
Learning systems
Hardness
Experiments
experiment
learning
performance
time

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Human-Computer Interaction
  • Education

Cite this

Nagano, K., Kawahara, Y., & Aihara, K. (2011). Size-constrained submodular minimization through minimum norm base. In Proceedings of the 28th International Conference on Machine Learning, ICML 2011 (pp. 977-984). (Proceedings of the 28th International Conference on Machine Learning, ICML 2011).

Size-constrained submodular minimization through minimum norm base. / Nagano, Kiyohito; Kawahara, Yoshinobu; Aihara, Kazuyuki.

Proceedings of the 28th International Conference on Machine Learning, ICML 2011. 2011. p. 977-984 (Proceedings of the 28th International Conference on Machine Learning, ICML 2011).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nagano, K, Kawahara, Y & Aihara, K 2011, Size-constrained submodular minimization through minimum norm base. in Proceedings of the 28th International Conference on Machine Learning, ICML 2011. Proceedings of the 28th International Conference on Machine Learning, ICML 2011, pp. 977-984, 28th International Conference on Machine Learning, ICML 2011, Bellevue, WA, United States, 6/28/11.
Nagano K, Kawahara Y, Aihara K. Size-constrained submodular minimization through minimum norm base. In Proceedings of the 28th International Conference on Machine Learning, ICML 2011. 2011. p. 977-984. (Proceedings of the 28th International Conference on Machine Learning, ICML 2011).
Nagano, Kiyohito ; Kawahara, Yoshinobu ; Aihara, Kazuyuki. / Size-constrained submodular minimization through minimum norm base. Proceedings of the 28th International Conference on Machine Learning, ICML 2011. 2011. pp. 977-984 (Proceedings of the 28th International Conference on Machine Learning, ICML 2011).
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