Efficient nearest-neighbor query and clustering of planar curves

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

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

ملخص

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.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيفAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
المحررونZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
ناشرSpringer Verlag
الصفحات28-42
عدد الصفحات15
رقم المعيار الدولي للكتب (المطبوع)9783030247652
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2019
منشور خارجيًانعم
الحدث16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, كندا
المدة: ٥ أغسطس ٢٠١٩٧ أغسطس ٢٠١٩

سلسلة المنشورات

الاسمLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
مستوى الصوت11646 LNCS
رقم المعيار الدولي للدوريات (المطبوع)0302-9743
رقم المعيار الدولي للدوريات (الإلكتروني)1611-3349

!!Conference

!!Conference16th International Symposium on Algorithms and Data Structures, WADS 2019
الدولة/الإقليمكندا
المدينةEdmonton
المدة٥/٠٨/١٩٧/٠٨/١٩

ملاحظة ببليوغرافية

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

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