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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.05127 |
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| _version_ | 1866910814502387712 |
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| author | Mizutani, Ryuhei |
| author_facet | Mizutani, Ryuhei |
| contents | This paper considers the minimization problem of relaxed submodular functions. For a positive integer $k$, a set function is called $k$-distant submodular if the submodular inequality holds for every pair whose symmetric difference is at least $k$. This paper provides a polynomial time algorithm to minimize $k$-distant submodular functions for a fixed positive integer $k$. This result generalizes the tractable result of minimizing 2/3-submodular functions, which satisfy the submodular inequality for at least two pairs formed from every distinct three sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Polynomial Algorithm for Minimizing $k$-Distant Submodular Functions Mizutani, Ryuhei Combinatorics This paper considers the minimization problem of relaxed submodular functions. For a positive integer $k$, a set function is called $k$-distant submodular if the submodular inequality holds for every pair whose symmetric difference is at least $k$. This paper provides a polynomial time algorithm to minimize $k$-distant submodular functions for a fixed positive integer $k$. This result generalizes the tractable result of minimizing 2/3-submodular functions, which satisfy the submodular inequality for at least two pairs formed from every distinct three sets. |
| title | A Polynomial Algorithm for Minimizing $k$-Distant Submodular Functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.05127 |