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

תקציר

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 מקורית אנגלית Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings Zachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack Springer Verlag 28-42 15 9783030247652 https://doi.org/10.1007/978-3-030-24766-9_3 פורסם - 2019 כן 16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, קנדהמשך הזמן: 5 אוג׳ 2019 → 7 אוג׳ 2019

סדרות פרסומים

שם Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 11646 LNCS 0302-9743 1611-3349

כנס

כנס 16th International Symposium on Algorithms and Data Structures, WADS 2019 קנדה Edmonton 5/08/19 → 7/08/19