Polynomial algorithm for $k$-partition minimization of monotone submodular function

Shohei Hidaka

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arXiv · 1802.01914

Polynomial algorithm for $k$-partition minimization of monotone submodular function

Shohei Hidaka

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Abstract

For a fixed $k$, this study considers $k$-partition minimization of submodular system $(V, f)$ with a finite set $V$ and symmetric submodular function $f: 2^{V} \mapsto \mathbb{R}$. Our algorithm uses the Queyranne's (1998) algorithm for 2-partition minimization which arises at each step of the recursive decomposition of subsets of the original $k$-partition minimization. We show that the computational complexity of this minimizer is $O(n^{3(k-1)})$.

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BibTeX RIS

Shohei Hidaka. 2018-02-06. Polynomial algorithm for $k$-partition minimization of monotone submodular function. https://arxiv.org/abs/1802.01914

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