Point enclosure problem for homothetic polygons

In this paper, we investigate the following problem: “given a set S of n homothetic polygons, preprocess S to efficiently report all the polygons of S containing a query point.” A set of polygons is said to be homothetic if each polygon can be obtained from any other polygon in the set using scaling...

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Vydáno v:Theoretical computer science Ročník 1030; s. 115054
Hlavní autoři: Akram, Waseem, Saxena, Sanjeev
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 13.03.2025
Témata:
Algorithms
Data structures
Dynamic algorithms
Geometric intersection
Data structures
Algorithms
Dynamic algorithms
Geometric intersection
ISSN:0304-3975
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Shrnutí:In this paper, we investigate the following problem: “given a set S of n homothetic polygons, preprocess S to efficiently report all the polygons of S containing a query point.” A set of polygons is said to be homothetic if each polygon can be obtained from any other polygon in the set using scaling and translation operations. The problem is a counterpart of the homothetic range search problem discussed by Chazelle and Edelsbrunner (1987) [9]. We show that after preprocessing a set of homothetic polygons with a constant number of vertices, queries can be answered in O(log⁡n+k) optimal time, where k is the output size. The preprocessing takes O(nlog⁡n) space and time. We also study the problem in a dynamic setting where insertion and deletion operations are allowed. The results we obtain also hold for c-oriented triangles, where c is a fixed constant.
ISSN:0304-3975
DOI:10.1016/j.tcs.2024.115054