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Minimum Dilation Triangulation in the Plane
, Ph.D. Dissertation Sharif University of Technology ; Izadi, Mohammad (Supervisor)
Abstract
If we consider a point set on the plane as the vertices and straight-line segments between them as the edges of a graph, and weight of each edge is equal to its Euclidean length, from this kind of graphs, triangulation is the graph with maximum number of the edges. In a triangulation, dilation of any two vertices is equal to the ratio of their shortest path length to their Euclidean distance, and dilation of the triangulation is defined as the maximum dilation of any pair of its vertices. Dilation is a characteristic that shows how much a triangulation approximates a complete graph. In the minimum dilation triangulation problem, the objective is to find a triangulation of a given set of...
Online Algorithms for Matching Points on the Plane
, M.Sc. Thesis Sharif University of Technology ; Zarrabizadeh, Hamid (Supervisor)
Abstract
Matching points is an important issue in the world of algorithms and has attracted the attention of many researchers with its wide applications. In recent years, researchers have proposed various issues in the field of matching points and looked at it from different perspectives. In recent years, this issue, like other issues, entered the online world and tried to be investigated online. In this thesis, we examine some examples of models of this problem that are projected on the plane and online and try to find a way to solve them or introduce a lower bound for them