Approximate nearest neighbor for curves - simple, efficient, and deterministic

Arnold Filtser, Omrit Filtser, Matthew J. Katz

פרסום מחקרי: פרק בספר / בדוח / בכנספרסום בספר כנסביקורת עמיתים

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 C0 ∈ C with δ(Q, C0) ≤ (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(1ε )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 מקוריתאנגלית
כותר פרסום המארח47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
עורכיםArtur Czumaj, Anuj Dawar, Emanuela Merelli
מוציא לאורSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
מסת"ב (אלקטרוני)9783959771382
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 1 יוני 2020
פורסם באופן חיצוניכן
אירוע47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, גרמניה
משך הזמן: 8 יולי 202011 יולי 2020

סדרות פרסומים

שםLeibniz International Proceedings in Informatics, LIPIcs
כרך168
ISSN (מודפס)1868-8969

כנס

כנס47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
מדינה/אזורגרמניה
עירVirtual, Online
תקופה8/07/2011/07/20

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).

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