Corpus ID: 119179035

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

@article{Hidaka2018PolynomialAF,
  title={Polynomial algorithm for \$k\$-partition minimization of monotone submodular function},
  author={Shohei Hidaka},
  journal={arXiv: Optimization and Control},
  year={2018}
}
  • S. Hidaka
  • Published 2018
  • Mathematics
  • arXiv: Optimization and Control
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 $O(n^{3(k-1)})$. 
1 Citations
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It is argued that the corresponding multiinformation function is a useful tool for problems concerning stochastic (conditional) dependence and independence (at least in the discrete case). Expand
Fast and exact search for the partition with minimal information loss
TLDR
A computationally efficient search to precisely identify the Minimum Information Partition among all possible partitions is proposed by exploiting the submodularity of the measure of information loss, when the measureof information loss is submodular. Expand