Hardness of Approximation for Morse Matching

@article{Bauer2019HardnessOA,
  title={Hardness of Approximation for Morse Matching},
  author={U. Bauer and A. Rathod},
  journal={ArXiv},
  year={2019},
  volume={abs/1801.08380}
}
We consider the approximability of maximization and minimization variants of the Morse matching problem, posed as open problems by Joswig and Pfetsch. We establish hardness results for Max-Morse matching and Min-Morse matching. In particular, we show that, for a simplicial complex with n simplices and dimension $d \leq 3$, it is NP-hard to approximate Min-Morse matching within a factor of $O(n^{1-\epsilon})$, for any $\epsilon > 0$. Moreover, using an L-reduction from Degree 3 Max-Acyclic… Expand
3 Citations
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