Finite Metric Spaces—Combinatories. Geometry and Algorithms
نویسنده
چکیده
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information. Metric spaces also come up in many recent advances in the theory of algorithms. Finally, finite submetrics of classical geometric objects such as normed spaces or manifolds reflect many important properties of the underlying structure. In this paper we review some of the recent advances in this area. 2000 Mathematics Subject Classification: Combinatorics, Algorithms, Geometry.
منابع مشابه
Metric and periodic lines in the Poincare ball model of hyperbolic geometry
In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.
متن کاملExtended graphs based on KM-fuzzy metric spaces
This paper, applies the concept of KM-fuzzy metric spaces and introduces a novel concept of KM-fuzzy metric graphs based on KM-fuzzy metric spaces. This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to extend the concept of KM-fuzzy metric spaces to a larger ...
متن کاملMetric Structures on Datasets: Stability and Classification of Algorithms
Several methods in data and shape analysis can be regarded as transformations between metric spaces. Examples are hierarchical clustering methods, the higher order constructions of computational persistent topology, and several computational techniques that operate within the context of data/shape matching under invariances. Metric geometry, and in particular different variants of the GromovHau...
متن کاملHermitian metric on quantum spheres
The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.
متن کاملGeometric Modeling of Dubins Airplane Movement and its Metric
The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...
متن کامل