COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
Scope & Guideline
Exploring Innovative Solutions in Computational Mathematics
Introduction
Aims and Scopes
- Geometric Algorithms:
Development and analysis of algorithms for solving geometric problems, including computational efficiency and theoretical foundations. - Geometric Structures:
Study of the properties and characteristics of various geometric structures such as polygons, polyhedra, and graphs. - Optimization Problems:
Exploration of optimization problems within geometric contexts, focusing on efficiency and effectiveness in computational solutions. - Graph Theory Applications:
Application of geometric principles to graph theory, including routing, connectivity, and geometric representations. - Topological and Combinatorial Geometry:
Investigating the relationships between topology, combinatorial structures, and geometric configurations. - Robotics and Motion Planning:
Addressing challenges in robotic movement and planning through geometric modeling and algorithms. - Data Structures for Geometric Queries:
Design and analysis of data structures to efficiently handle queries related to geometric data.
Trending and Emerging
- Dynamic and Online Algorithms:
There is a growing focus on algorithms that handle dynamic data and online scenarios, reflecting the needs of real-time applications. - Algorithmic Applications in Robotics:
Emerging themes in robotic motion planning and geometric modeling are gaining attention, highlighting the intersection of computation and robotics. - Geometric Data Structures for Big Data:
Research into efficient data structures for handling large geometric datasets is on the rise, driven by advancements in data science and analytics. - Topological Data Analysis:
Increasing interest in applying topological concepts to geometric problems, particularly in analyzing shapes and structures from data. - Geometric Machine Learning:
The incorporation of machine learning techniques into geometric problems is becoming prominent, reflecting the interdisciplinary nature of current research.
Declining or Waning
- Static Geometric Problems:
Research focusing on static geometric problems has decreased, possibly due to the increasing interest in dynamic and online algorithms. - Classical Geometric Constructions:
The emphasis on classical constructions and theoretical proofs has waned in favor of more applied and computational aspects of geometry. - Low-Dimensional Geometry:
There appears to be a reduced focus on low-dimensional geometric problems as researchers explore higher-dimensional applications and complexities. - Basic Geometric Properties:
Basic studies of geometric properties without computational implications are less frequent, as the journal shifts towards more complex and applicable geometric theories.
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