Question

Describe the maxima set problem solution: Given a set of n distinct points on a 2D plane find the set of all the maximum points

Answer 1

The maxima set problem solution involves sorting n distinct points in a 2D plane, scanning them to find maximal points, and producing a set that contains no points dominated by others.

Step-by-step explanation:

The maxima set problem in computational geometry is concerned with finding a subset of points from a given set of n distinct points in a 2D plane, such that no point in the maxima set is dominated by any other point in the entire set. A point is said to dominate another if it is greater than or equal to the other point in all dimensions. To solve the maxima set problem, we can follow a step-by-step approach:

1. Sort the points in decreasing order of one coordinate (commonly the x-coordinate).
2. Scan through the sorted points and maintain the maximum value found so far for the other coordinate (y-coordinate).
3. If a point has the second coordinate (y-coordinate) greater than the maximum so far, it is a maximal point, so we add it to the maxima set and update the maximum value of the second coordinate.
4. Continue scanning until all points have been processed.

The resulting set of points is the maxima set where no point within the set is dominated by any other point from the original set of n points.