English

Three-dimensional matching is NP-Hard

Computational Complexity 2020-03-03 v1

Abstract

The standard proof of NP-Hardness of 3DM provides a power-44 reduction of 3SAT to 3DM. In this note, we provide a linear-time reduction. Under the exponential time hypothesis, this reduction improves the runtime lower bound from 2o(m4)2^{o(\sqrt[4]{m})} (under the standard reduction) to 2o(m)2^{o(m)}.

Keywords

Cite

@article{arxiv.2003.00336,
  title  = {Three-dimensional matching is NP-Hard},
  author = {Shrinu Kushagra},
  journal= {arXiv preprint arXiv:2003.00336},
  year   = {2020}
}
R2 v1 2026-06-23T13:58:57.052Z