Geometric Algorithms for Covering a Point Set

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Hajiaghaei Shanjani, Sima | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47023 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
Covering problem is an interesting problem in computational geometry. In this problem, a geometric object and/or its location should be found for a set of points that encloses the points while optimizing an objective function such as area, perimeter, surface area, and volume. Minimum enclosing circle and minimum enclosing box are well-known problems in this ﬁeld. According to the constraints of the problem, different types of this problem can be deﬁned and utilized in many applications like geometric information systems (GIS), military and communication systems.Geometric algorithms for solving some special covering problems are found in this thesis. The problems involve using two or more known geometric objects to enclose the points. For instance, the problem of covering a point set by two rectangles, known as two-rectangle covering, is analyzed for minimizing the summation of rectangles’ areas. Then, the new results for the case of covering points by two triangles are presented. Approximation and exact algorithms are found for two arbitrary triangles covering problem. More arbitrary triangles, two isosceles triangles, as well as two ﬁxed-angle triangles are also investigated
Keywords:
Computational Geometry ; Approximate Algorithm ; Points Covering ; Points Covering with Triangle