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In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. [1] That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the ...
Testing for compositeness is known to be in P, but the complexity of the closely related integer factorization problem remains open. Minimum length triangulation [ 8 ] Problem 12 is known to be NP-hard, but it is unknown if it is in NP.
Minimum-weight triangulation is a triangulation in which the goal is to minimize the total edge length. A point-set triangulation is a polygon triangulation of the convex hull of a set of points. A Delaunay triangulation is another way to create a triangulation based on a set of points.
Frequently used and studied point set triangulations include the Delaunay triangulation (for points in general position, the set of simplices that are circumscribed by an open ball that contains no input points) and the minimum-weight triangulation (the point set triangulation minimizing the sum of the edge lengths).
The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of the same points, [22] and this can be exploited to compute it efficiently. For modelling terrain or other objects given a point cloud , the Delaunay triangulation gives a nice set of triangles to use as polygons in the model.
It returns a spanning arborescence rooted at of minimum weight, where the weight of an arborescence is defined to be the sum of its edge weights, () = (). The algorithm has a recursive description. Let f ( D , r , w ) {\displaystyle f(D,r,w)} denote the function which returns a spanning arborescence rooted at r {\displaystyle r} of minimum weight.
The minimum weight is a concept used in various branches of mathematics and computer science related to measurement. Minimum Hamming weight, a concept in coding theory; Minimum weight spanning tree; Minimum-weight triangulation, a topic in computational geometry and computer science
The circle-based 1.1-skeleton (heavy dark edges) and 0.9-skeleton (light dashed blue edges) of a set of 100 random points in a square. In computational geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean plane.