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Approximation algorithms for Max Morse Matching

Rathod, Abhishek and Bin Masood, Talha and Natarajan, Vijay (2017) Approximation algorithms for Max Morse Matching. In: COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 61 . pp. 1-23.

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Official URL: http://dx.doi.org/10.1016/j.comgeo.2016.10.002

Abstract

In this paper, we prove that the Max Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch 1]. For D-dimensional simplicial complexes, we obtain a (D+1)/(D-2+D+1)-factor approximation ratio using a simple edge reorientation algorithm that removes cycles. For D >= 5, we describe a 2/D-factor approximation algorithm for simplicial manifolds by processing the simplices in increasing order of dimension. This algorithm leads to 1/2-factor approximation for 3-manifolds and 4/9-factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a 1/(D+1)-factor approximation ratio. 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. (C) 2016 Elsevier B.V. All rights reserved.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 09 Mar 2017 06:04
Last Modified: 09 Mar 2017 06:04
URI: http://eprints.iisc.ernet.in/id/eprint/56352

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