NP-Hardness of Tensor Network Contraction Ordering
Abstract
We study the optimal order (or sequence) of contracting a tensor network with a minimal computational cost. We conclude 2 different versions of this optimal sequence: that minimize the operation number (OMS) and that minimize the time complexity (CMS). Existing results only shows that OMS is NP-hard, but no conclusion on CMS problem. In this work, we firstly reduce CMS to CMS-0, which is a sub-problem of CMS with no free indices. Then we prove that CMS is easier than OMS, both in general and in tree cases. Last but not least, we prove that CMS is still NP-hard. Based on our results, we have built up relationships of hardness of different tensor network contraction problems.
Keywords
Cite
@article{arxiv.2310.06140,
title = {NP-Hardness of Tensor Network Contraction Ordering},
author = {Jianyu Xu and Hanwen Zhang and Ling Liang and Lei Deng and Yuan Xie and Guoqi Li},
journal= {arXiv preprint arXiv:2310.06140},
year = {2023}
}
Comments
Jianyu Xu and Hanwen Zhang are equal contributors. 10 pages (reference and appendix excluded), 20 pages in total, 6 figures