### Abstract

Original language | English |
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Title of host publication | Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019 |

Place of Publication | Philadelphia |

Publisher | SIAM - Society of Industrial and Applied Mathematics |

Pages | 2675-2688 |

Publication status | Published - 2019 |

Event | 30th Annual ACM-SIAM Symposium on Discrete Algorithms - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019 |

### Conference

Conference | 30th Annual ACM-SIAM Symposium on Discrete Algorithms |
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Abbreviated title | SODA '19 |

Country | United States |

City | San Diego |

Period | 6/01/19 → 9/01/19 |

### Fingerprint

### Fields of Expertise

- Information, Communication & Computing

### Cite this

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

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*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, pp. 2675-2688, 30th Annual ACM-SIAM Symposium on Discrete Algorithms , San Diego, United States, 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 -