Dominance for enclosure problems

Two triangles in the plane are called homothetic if one can be obtained from the other using scaling and translation operations. In this paper, we investigate an enclosure problem involving homothetic triangles. Specifically, the problem is to preprocess a given set of n homothetic triangles so that...

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Veröffentlicht in:Journal of combinatorial optimization Jg. 50; H. 4; S. 41
Hauptverfasser: Akram, Waseem, Saxena, Sanjeev
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2025
Springer Nature B.V
Schlagworte:
Algorithms
Combinatorics
Convex and Discrete Geometry
Enclosures
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polygons
Queries
Searching
Theory of Computation
Trapezoids
Dominance
Data structures
Algorithms
Geometric intersection
ISSN:1382-6905, 1573-2886
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Zusammenfassung:Two triangles in the plane are called homothetic if one can be obtained from the other using scaling and translation operations. In this paper, we investigate an enclosure problem involving homothetic triangles. Specifically, the problem is to preprocess a given set of n homothetic triangles so that the triangles enclosing (or containing) a query object can be found quickly. The query objects we consider include points, line segments, trapezoids, and ellipses. We propose an efficient solution to the problem using the 3-D dominance searching. Our results can also be extended to higher dimensions. Moreover, we also present a negative result that suggests that the enclosure problem involving (arbitrarily) axis-parallel right-angled triangles may not be solvable using 4-D dominance searching.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-025-01373-5