Approximation algorithms for Max Morse Matching

Abhishek Rathod; Talha Bin Masood; Vijay Natarajan

doi:10.1016/j.comgeo.2016.10.002

Approximation algorithms for Max Morse Matching

Abhishek Rathod
, Talha Bin Masood
, Vijay Natarajan

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 -factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a -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.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Computational Geometry: Theory and Applications
Volume	61
DOIs	https://doi.org/10.1016/j.comgeo.2016.10.002
State	Published - 1 Feb 2017
Externally published	Yes

Keywords

Approximation algorithms
Computational topology
Discrete Morse theory
Homology computation

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2016.10.002

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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 [1]. For D-dimensional simplicial complexes, we obtain a -factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a -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.",

keywords = "Approximation algorithms, Computational topology, Discrete Morse theory, Homology computation",

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AU - Rathod, Abhishek

AU - Bin Masood, Talha

AU - Natarajan, Vijay

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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 -factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a -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.

AB - 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 -factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a -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.

KW - Approximation algorithms

KW - Computational topology

KW - Discrete Morse theory

KW - Homology computation

UR - https://www.scopus.com/pages/publications/84994852917

U2 - 10.1016/j.comgeo.2016.10.002

DO - 10.1016/j.comgeo.2016.10.002

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SP - 1

EP - 23

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

ER -

Approximation algorithms for Max Morse Matching

Abstract

Keywords

ASJC Scopus subject areas

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