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arXiv · 1604.04707

Approximation Algorithms for Max-Morse Matching

Abhishek Rathod·Talha Bin Masood·Vijay Natarajan
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Abstract

In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For $D$-dimensional simplicial complexes, we obtain a $\frac{(D+1)}{(D^2+D+1)}$-factor approximation ratio using a simple edge reorientation algorithm that removes cycles. Our second result is an algorithm that provides a $\frac{2}{D}$-factor approximation for simplicial manifolds by processing the simplices in increasing order of dimension. One application of these algorithms is towards efficient homology computation of simplicial complexes. Experiments using a prototype implementation on several datasets indicate that the algorithm computes near optimal results.

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Abhishek Rathod, Talha Bin Masood, Vijay Natarajan. 2016-04-16. Approximation Algorithms for Max-Morse Matching. https://arxiv.org/abs/1604.04707

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