Related papers: Applications of topology in computer algorithms
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Representing a scanned map of the real environment as a topological structure is an important research in robotics. %is currently an important research. Since topological representations of maps save a huge amount of map storage space and…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of…
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
In the algorithm selection research, the discussion surrounding algorithm features has been significantly overshadowed by the emphasis on problem features. Although a few empirical studies have yielded evidence regarding the effectiveness…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…
For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With…
Development of routing algorithms is of clear importance as the volume of Internet traffic continues to increase. In this survey, there is much research into how Machine Learning techniques can be employed to improve the performance and…
I discuss the evolution of computer architectures with a focus on QCD and with reference to the interplay between architecture, engineering, data motion and algorithms. New architectures are discussed and recent performance results are…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this…
When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for…