In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized.
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output are random variables.
Markus Hendrik Overmars is a Dutch computer scientist and teacher of game programming known for his game development application GameMaker. GameMaker lets people create computer games using a drag-and-drop interface. He is the former head of the Center for Geometry, Imaging, and Virtual Environments at Utrecht University, in the Netherlands. This research center concentrates on computational geometry and its application in areas like computer graphics, robotics, geographic information systems, imaging, multimedia, virtual environments, and games.
In computational geometry and robot motion planning, a visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents a point location, and each edge represents a visible connection between them. That is, if the line segment connecting two locations does not pass through any obstacle, an edge is drawn between them in the graph. When the set of locations lies in a line, this can be understood as an ordered series. Visibility graphs have therefore been extended to the realm of time series analysis.
In geometry, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction as C at these points. That is, L is a tangent line at P and at Q.
Motion planning, also path planning is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is used in computational geometry, computer animation, robotics and computer games.
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values.
In geometry, visibility is a mathematical abstraction of the real-life notion of visibility.
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles.
A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. The tree is constructed incrementally from samples drawn randomly from the search space and is inherently biased to grow towards large unsearched areas of the problem. RRTs were developed by Steven M. LaValle and James J. Kuffner Jr. They easily handle problems with obstacles and differential constraints and have been widely used in autonomous robotic motion planning.
Jean-Claude Latombe is a French-American roboticist and the Kumagai Professor Emeritus in the School of Engineering at Stanford University. Latombe is a researcher in robot motion planning, and has authored one of the most highly cited books in the field.
Any-angle path planning algorithms are pathfinding algorithms that search for a Euclidean shortest path between two points on a grid map while allowing the turns in the path to have any angle. The result is a path that cuts directly through open areas and has relatively few turns. More traditional pathfinding algorithms such as A* either lack in performance or produce jagged, indirect paths.
For robot control, Stochastic roadmap simulation is inspired by probabilistic roadmap methods (PRM) developed for robot motion planning.
Lydia E. Kavraki is a Greek-American computer scientist, the Noah Harding Professor of Computer Science, a professor of bioengineering, electrical and computer engineering, and mechanical engineering at Rice University. She is also the director of the Ken Kennedy Institute at Rice University. She is known for her work on robotics/AI and bioinformatics/computational biology and in particular for the probabilistic roadmap method for robot motion planning and biomolecular configuration analysis.
OMPL is a software package for computing motion plans using sampling-based algorithms. The content of the library is limited to motion planning algorithms, which means there is no environment specification, no collision detection or visualization. This is intentional as the library is designed to be easily integrated into systems that already provide the additional needed components. For example, OMPL is integrated with ROS and MoveIt!. In 2012 OMPL won the Grand Prize at the Open Source Software World Challenge.
Nancy Marie Amato is an American computer scientist noted for her research on the algorithmic foundations of motion planning, computational biology, computational geometry and parallel computing. Amato is the Abel Bliss Professor of Engineering and Head of the Department of Computer Science at the University of Illinois at Urbana-Champaign. Amato is noted for her leadership in broadening participation in computing, and is currently a member of the steering committee of CRA-WP, of which she has been a member of the board since 2000.
Real-Time Path Planning is a term used in robotics that consists of motion planning methods that can adapt to real time changes in the environment. This includes everything from primitive algorithms that stop a robot when it approaches an obstacle to more complex algorithms that continuously takes in information from the surroundings and creates a plan to avoid obstacles.
In network theory, link prediction is the problem of predicting the existence of a link between two entities in a network. Examples of link prediction include predicting friendship links among users in a social network, predicting co-authorship links in a citation network, and predicting interactions between genes and proteins in a biological network. Link prediction can also have a temporal aspect, where, given a snapshot of the set of links at time , the goal is to predict the links at time . Link prediction is widely applicable. In e-commerce, link prediction is often a subtask for recommending items to users. In the curation of citation databases, it can be used for record deduplication. In bioinformatics, it has been used to predict protein-protein interactions (PPI). It is also used to identify hidden groups of terrorists and criminals in security related applications.
