Efficient nearest-neighbor query and clustering of planar curves

Boris Aronov, Omrit Filtser, Michael Horton, Matthew J. Katz, Khadijeh Sheikhan

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


We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let C be a set of n polygonal curves, each of size m. In the nearest-neighbor problem, the goal is to construct a compact data structure over C, such that, given a query curve Q, one can efficiently find the curve in C closest to Q. In the center problem, the goal is to find a curve Q, such that the maximum distance between Q and the curves in C is minimized. We use the well-known discrete Fréchet distance function, both under L and under L2, to measure the distance between two curves. For the nearest-neighbor problem, despite discouraging previous results, we identify two important cases for which it is possible to obtain practical bounds, even when m and n are large. In these cases, either Q is a line segment or C consists of line segments, and the bounds on the size of the data structure and query time are nearly linear in the size of the input and query curve, respectively. The returned answer is either exact under L, or approximated to within a factor of 1 + ε under L2. We also consider the variants in which the location of the input curves is only fixed up to translation, and obtain similar bounds, under L. As for the center problem, we study the case where the center is a line segment, i.e., we seek the line segment that represents the given set as well as possible. We present near-linear time exact algorithms under L, even when the location of the input curves is only fixed up to translation. Under L2, we present a roughly O(n2m3) -time exact algorithm.

שפה מקוריתאנגלית
כותר פרסום המארחAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
עורכיםZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
מוציא לאורSpringer Verlag
מספר עמודים15
מסת"ב (מודפס)9783030247652
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 2019
פורסם באופן חיצוניכן
אירוע16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, קנדה
משך הזמן: 5 אוג׳ 20197 אוג׳ 2019

סדרות פרסומים

שםLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
כרך11646 LNCS
ISSN (מודפס)0302-9743
ISSN (אלקטרוני)1611-3349


כנס16th International Symposium on Algorithms and Data Structures, WADS 2019

הערה ביבליוגרפית

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

טביעת אצבע

להלן מוצגים תחומי המחקר של הפרסום 'Efficient nearest-neighbor query and clustering of planar curves'. יחד הם יוצרים טביעת אצבע ייחודית.

פורמט ציטוט ביבליוגרפי