## תקציר

In the (1 + ε, r)-approximate near-neighbor problem for curves (ANNC) under some similarity measure δ, the goal is to construct a data structure for a given set C of curves that supports approximate near-neighbor queries: Given a query curve Q, if there exists a curve C ∈ C such that δ(Q, C) ≤ r, then return a curve C^{0} ∈ C with δ(Q, C^{0}) ≤ (1 + ε)r. There exists an efficient reduction from the (1 + ε)-approximate nearest-neighbor problem to ANNC, where in the former problem the answer to a query is a curve C ∈ C with δ(Q, C) ≤ (1 + ε) · δ(Q, C^{∗}), where C^{∗} is the curve of C most similar to Q. Given a set C of n curves, each consisting of m points in d dimensions, we construct a data structure for ANNC that uses n · O(^{1}_{ε} )^{md} storage space and has O(md) query time (for a query curve of length m), where the similarity measure between two curves is their discrete Fréchet or dynamic time warping distance. Our method is simple to implement, deterministic, and results in an exponential improvement in both query time and storage space compared to all previous bounds. Further, we also consider the asymmetric version of ANNC, where the length of the query curves is k m, and obtain essentially the same storage and query bounds as above, except that m is replaced by k. Finally, we apply our method to a version of approximate range counting for curves and achieve similar bounds.

שפה מקורית | אנגלית |
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כותר פרסום המארח | 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 |

עורכים | Artur Czumaj, Anuj Dawar, Emanuela Merelli |

מוציא לאור | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

מסת"ב (אלקטרוני) | 9783959771382 |

מזהי עצם דיגיטלי (DOIs) | |

סטטוס פרסום | פורסם - 1 יוני 2020 |

פורסם באופן חיצוני | כן |

אירוע | 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, גרמניה משך הזמן: 8 יולי 2020 → 11 יולי 2020 |

### סדרות פרסומים

שם | Leibniz International Proceedings in Informatics, LIPIcs |
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כרך | 168 |

ISSN (מודפס) | 1868-8969 |

### כנס

כנס | 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 |
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מדינה/אזור | גרמניה |

עיר | Virtual, Online |

תקופה | 8/07/20 → 11/07/20 |

### הערה ביבליוגרפית

Publisher Copyright:© Arnold Filtser, Omrit Filtser, and Matthew J. Katz; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).