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arXiv · 2407.05127

A Polynomial Algorithm for Minimizing $k$-Distant Submodular Functions

Ryuhei Mizutani
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Abstract

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.

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Ryuhei Mizutani. 2024-07-06. A Polynomial Algorithm for Minimizing $k$-Distant Submodular Functions. https://arxiv.org/abs/2407.05127

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