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Computational And Combinatorial Problems On Some Geometric Proximity Graphs
(2017-05-24)
In this thesis, we focus on the study of computational and combinatorial problems on various geometric proximity graphs. Delaunay and Gabriel graphs are widely studied geometric proximity structures. These graphs have been ...
Delaunay Graphs for Various Geometric Objects
(2017-12-12)
Given a set of n points P ⊂ R2, the Delaunay graph of P for a family of geometric objects C is a graph defined as follows: the vertex set is P and two points p, p' ∈ P are connected by an edge if and only if there exists ...
Module Grobner Bases Over Fields With Valuation
(2017-07-12)
Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical ...