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 ...

Scalar fields are used to represent physical quantities measured over a domain of interest. Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights ...

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 ...

A range space (P, S) consists of a set P of n elements and a collection S = {S1,...,Sm} of subsets of P , referred to as ranges. A hitting set for this range space refers to a subset H of P such that every Si in S contains ...

In this thesis we consider extensions and generalizations of some classical problems in Combinatorial Geometry. Our work is an offshoot of four classical problems in Combinatorial Geometry. A fundamental assumption in these ...

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 ...

Consider an app on a smartphone which displays local business ads. When a user opens the app, then k local business ads need to displayed (where k would typically be 3 or 5) such that the profit made by the app is ...

We study the Maximum Independent Set of Rectangles (MISR) problem. The problem involves a collection of n axis-parallel rectangles in 2D with weights. For the unweighted case, the goal is to find the maximum number of ...