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The fair polygon partitioning problem [20] is to partition a (convex) polygon into (convex) pieces with an equal perimeter and equal area (this is a special case of fair cake-cutting). Any convex polygon can be easily cut into any number n of convex pieces with an area of exactly 1/n. However, ensuring that the pieces have both equal area and ...
The Robertson–Webb query model – in which the algorithm may ask each agent a query of one of two kinds: "evaluate a given piece of cake" or "mark a piece of cake with a given value". The Moving-knives model – in which the algorithm continuously moves one or more knives above the cake until some agents shout "stop".
This number is given by the 5th Catalan number. It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other non-nearest neighbor vertices. The total number of ways to triangulate a convex n-gon by non-intersecting diagonals is the (n−2)nd Catalan number, which equals
For a given set of points S = {p 1, p 2, ..., p n}, the farthest-point Voronoi diagram divides the plane into cells in which the same point of P is the farthest point. A point of P has a cell in the farthest-point Voronoi diagram if and only if it is a vertex of the convex hull of P .
The region quadtree represents a partition of space in two dimensions by decomposing the region into four equal quadrants, subquadrants, and so on with each leaf node containing data corresponding to a specific subregion. Each node in the tree either has exactly four children, or has no children (a leaf node).
Not many three-dimensional (3D) applications involving cutting are known; however the closely related 3D packing problem has many industrial applications, such as packing objects into shipping containers (see e.g. containerization: the related sphere packing problem has been studied since the 17th century (Kepler conjecture)).
As you progress through levels, your job will become more difficult, as you may need to split a shape into more than just two equal pieces, and the shapes themselves become more intricate, moving ...
In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or ...