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The task is then to find a minimum cardinality subset of left-vertices that has a non-trivial intersection with each of the right-vertices, which is precisely the hitting set problem. In the field of computational geometry, a hitting set for a collection of geometrical objects is also called a stabbing set or piercing set. [5]
Let Q k be the intersection of the bisectors in the k-th pair. The line q in the p 1 direction is placed to go through an intersection Q x such that there are intersections in each half-plane defined by the line (median position). The constrained version of the enclosing problem is run on the line q' which determines half-plane where the center ...
So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist. However, when restricted to the context of subsets of a given fixed set X {\displaystyle X} , the notion of the intersection of an empty collection of ...
A special case of this method is the use of the modular product of graphs to reduce the problem of finding the maximum common induced subgraph of two graphs to the problem of finding a maximum clique in their product. [7] In automatic test pattern generation, finding cliques can help to bound the size of a test set. [8]
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.
In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, [1] allows for multiple instances for each of its elements.The number of instances given for each element is called the multiplicity of that element in the multiset.
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...