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Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…
Euler diagrams are a tool for the graphical representation of set relations. Due to their simple way of visualizing elements in the sets by geometric containment, they are easily readable by an inexperienced reader. Euler diagrams where the…
We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…
The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…
In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…
Given a bichromatic point set $P=\textbf{R} \cup \textbf{B}$ of red and blue points, a separator is an object of a certain type that separates $\textbf{R}$ and $\textbf{B}$. We study the geometric separability problem when the separator is…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on…
The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
This is a comparative study of the traditional 3D computer graphics technique of geometric modelling and image-based rendering techniques that were surveyed and implemented.We have discussed the classifications and representative methods of…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
An increased interest in immersive applications has drawn attention to emerging 3D imaging representation formats, notably light fields and point clouds (PCs). Nowadays, PCs are one of the most popular 3D media formats, due to recent…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Duality quantum computing (DQC) offers the use of linear combination of unitaries (LCU), or generalized quantum gates, in designing quantum algorithms. DQC contains wave divider and wave combiner operations. The wave function of a quantum…
In order to satisfy timing constraints, modern real-time applications require massively parallel accelerators such as General Purpose Graphic Processing Units (GPGPUs). Generation after generation, the number of computing clusters made…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
The Neural GPU is a recent model that can learn algorithms such as multi-digit binary addition and binary multiplication in a way that generalizes to inputs of arbitrary length. We show that there are two simple ways of improving the…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…