Computational geometry coresets

  • What is the use of computational geometry?

    Other important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), and computer-aided engineering (CAE)..

  • Coresets are weighted subsets of the data, which guarantee that models fitting the coreset also provide a good fit for the original data.
In computational geometry, a coreset is a small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets (such as their minimum bounding box volume) results in approximately equal numbers.
In computational geometry, a coreset is a small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets (such as their minimum bounding box volume) results in approximately equal numbers.
In computational geometry, a coreset is a small set of points that approximates the shape of a larger point set, in the sense that applying some geometric 

Computational geometry concept

In computational geometry, a coreset is a small set of points that approximates the shape of a larger point set, in the sense that applying some geometric measure to the two sets results in approximately equal numbers.
Many natural geometric optimization problems have coresets that approximate an optimal solution to within a factor of texhtml >1 + ε, that can be found quickly, and that have size bounded by a function of texhtml >1/ε independent of the input size, where texhtml >ε is an arbitrary positive number.
When this is the case, one obtains a linear-time or near-linear time approximation scheme, based on the idea of finding a coreset and then applying an exact optimization algorithm to the coreset.
Regardless of how slow the exact optimization algorithm is, for any fixed choice of texhtml >ε, the running time of this approximation scheme will be texhtml >O(1) plus the time to find the coreset.

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