Convex Hull operation not specific enough

What is the problem on convex hull?

The convex hull of the set of points Q is the convex polygon P that encompasses all of the points given. The problem of finding the smallest polygon P such that all the points of set Q are either on the boundary of P or inside P is known as the convex hull problem.
 

What is the complexity of convex hull problem using divide and conquer?

What is the time complexity to solve the convex hull problem? It takes O(n³) time using the brute force approach, whereas the divide and conquer approach takes O(n) time to find the convex hull.
 

Is a convex hull unique?

This leads to an alternative definition of the convex hull of a finite set P P P of points in the plane: it is the unique convex polygon whose vertices are points from P P P and which contains all points of P P P. The set of green nails are the convex hull of the collection of the points.

What is the extreme point of a convex hull?

Extreme points



An extreme point of a convex set is a point in the set that does not lie on any open line segment between any other two points of the same set. For a convex hull, every extreme point must be part of the given set, because otherwise it cannot be formed as a convex combination of given points.

How can we solve a convex optimization problem?

Convex optimization problems can also be solved by the following contemporary methods: Bundle methods (Wolfe, Lemaréchal, Kiwiel), and. Subgradient projection methods (Polyak), Interior-point methods, which make use of self-concordant barrier functions and self-regular barrier functions.

Is convex hull NP hard?

We prove that approximating the convex hull in this manner in the plane can be solved by either a simple graph based or dynamic programming based algorithm in polynomial time. Complementing this result we show that in three dimensions and higher the problem is NP-hard.

What are the disadvantages of convex hull?

The disadvantages of using the Divide and Conquer approach towards Convex Hull is as follows: Recursion which is the basis of divide and conquer is slow, the overhead of the repeated subroutine calls , along with that of storing the call stack.

What is the limitation of divide and conquer technique?

Disadvantages of Divide and Conquer



Since most of its algorithms are designed by incorporating recursion, so it necessitates high memory management. An explicit stack may overuse the space. It may even crash the system if the recursion is performed rigorously greater than the stack present in the CPU.

Which is the fastest convex hull?

Its idea is based on the quicksort algorithm and as the quicksort is frequently the fastest among sorting algorithms, the quickhull algorithm tends to be the fastest among the convex hull algorithms for points.
 

What is a convex problem in machine learning?

A convex function refers to a function whose graph is shaped like a cup U. A twice differential function of single variable is convex if and only if its second derivate is non-negative. Example: quadratic function (x^2)

What is the other name for convex hull problem?

Explanation: The other name for quick hull problem is convex hull problem whereas the closest pair problem is the problem of finding the closest distance between two points.

What is the time complexity of convex hull problem?

It has O(nh) time complexity, where n is the number of points in the set, and h is the number of points in the hull. In the worst case the complexity is Θ(n²).