### Abstract

Dynamic Time Warping (DTW) is a well-known similarity measure for curves, i.e., sequences of points, and especially for time series. We study several proximity problems for curves, where dynamic time warping is the underlying similarity measure. More precisely, we focus on the variants of these problems, in which, whenever we refer to the dynamic time warping distance between two curves, one of them is a line segment (i.e., a sequence of length two). These variants already reveal some of the difficulties that occur when dealing with the more general ones. Specifically, we study the following three problems: (i) distance oracle: given a curve C in R^{d}, preprocess it to accommodate distance computations between query segments and C, (ii) segment center: given a set C of curves in R^{d}, find a segment s that minimizes the maximum distance between s and a curve in C, and (iii) segment nearest neighbor: given C, construct a data structure for segment nearest neighbor queries, i.e., return the curve in C which is closest to a query segment s. We present solutions to these problems in any constant dimension d ≥ 1, using L∞ for inter-point distances. We also consider the approximation version of the first problem, using L1 for inter-point distances. That is, given a length-m curve C in R^{d}, we construct a data structure of size O(m log m) that allows one to compute a 2-approximation of the distance between a query segment s and C in O(log^{3} m) time. Finally, we describe an interesting experimental study that we performed, which is related to the first problem above.

Original language | English (US) |
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Title of host publication | 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 |

Editors | Javier Esparza, Daniel Kral�, Daniel Kral� |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771597 |

DOIs | |

State | Published - Aug 1 2020 |

Event | 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 - Prague, Czech Republic Duration: Aug 25 2020 → Aug 26 2020 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 170 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 |
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Country | Czech Republic |

City | Prague |

Period | 8/25/20 → 8/26/20 |

### Keywords

- Clustering
- Distance oracle
- Dynamic time warping
- Nearest-neighbor search

### ASJC Scopus subject areas

- Software

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## Cite this

*45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020*[MFCS-2020-9] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 170). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2020.9