### Abstract

Originalsprache | englisch |
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Titel | Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019 |

Erscheinungsort | Philadelphia |

Herausgeber (Verlag) | SIAM - Society of Industrial and Applied Mathematics |

Seiten | 2675-2688 |

Publikationsstatus | Veröffentlicht - 2019 |

Veranstaltung | 30th Annual ACM-SIAM Symposium on Discrete Algorithms - San Diego, USA / Vereinigte Staaten Dauer: 6 Jan 2019 → 9 Jan 2019 |

### Konferenz

Konferenz | 30th Annual ACM-SIAM Symposium on Discrete Algorithms |
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Kurztitel | SODA '19 |

Land | USA / Vereinigte Staaten |

Ort | San Diego |

Zeitraum | 6/01/19 → 9/01/19 |

### Fingerprint

### Fields of Expertise

- Information, Communication & Computing

### Dies zitieren

*Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019*(S. 2675-2688). Philadelphia: SIAM - Society of Industrial and Applied Mathematics.

**Improved Topological Approximations by Digitization.** / Choudhary, Aruni; Kerber, Michael; Raghvendra, Sharath.

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Forschung › Begutachtung

*Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019.*SIAM - Society of Industrial and Applied Mathematics, Philadelphia, S. 2675-2688, San Diego, USA / Vereinigte Staaten, 6/01/19.

}

TY - GEN

T1 - Improved Topological Approximations by Digitization

AU - Choudhary, Aruni

AU - Kerber, Michael

AU - Raghvendra, Sharath

PY - 2019

Y1 - 2019

N2 - Čech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becomes prohibitively expensive for large-sized data sets even for medium-to-low dimensional data. We present an approximation scheme for (1 + ε)-approximating the topological information of the Čech complexes for n points in Rd, for ε ∈ (0, 1]. Our approximation has a total size of [MATH HERE] for constant dimension d, improving all the currently available (1 + ε)-approximation schemes of simplicial filtrations in Euclidean space. Perhaps counter-intuitively, we arrive at our result by adding additional [MATH HERE] sample points to the input. We achieve a bound that is independent of the spread of the point set by pre-identifying the scales at which the Čech complexes changes and sampling accordingly.

AB - Čech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becomes prohibitively expensive for large-sized data sets even for medium-to-low dimensional data. We present an approximation scheme for (1 + ε)-approximating the topological information of the Čech complexes for n points in Rd, for ε ∈ (0, 1]. Our approximation has a total size of [MATH HERE] for constant dimension d, improving all the currently available (1 + ε)-approximation schemes of simplicial filtrations in Euclidean space. Perhaps counter-intuitively, we arrive at our result by adding additional [MATH HERE] sample points to the input. We achieve a bound that is independent of the spread of the point set by pre-identifying the scales at which the Čech complexes changes and sampling accordingly.

M3 - Conference contribution

SP - 2675

EP - 2688

BT - Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019

PB - SIAM - Society of Industrial and Applied Mathematics

CY - Philadelphia

ER -