geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping...

a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping)...

given a set of locations in a map, find a maximum set of disjoint rectangular labels near these locations. Finding a maximum independent set in intersection...

pairwise disjoint in polynomial time. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in...

{\displaystyle n=2^{(k+1)}-2} elements. The set system consists of k {\displaystyle k} pairwise disjoint sets S 1 , … , S k {\displaystyle S_{1},\ldots...

Fuzzy sets are disjoint if and only if their supports are disjoint according to the standard definition for crisp sets. For disjoint fuzzy sets A , B...

the maximum flow is k {\displaystyle k} iff there are k {\displaystyle k} edge-disjoint paths. 2. The paths must be independent, i.e., vertex-disjoint (except...

closed under complements and countable disjoint unions π-system – Family of sets closed under intersection Ring of sets – Family closed under unions and relative...

the feedback arc set problem obeys a min-max theorem: the minimum size of a feedback arc set equals the maximum number of edge-disjoint directed cycles...

G {\displaystyle G} are pairwise disjoint (meaning, disjoint from X {\displaystyle X} and from each other). The set of those translates partitions the...

notation was utilized in definitions; for example, Cantor defined two sets as being disjoint if their intersection has an absence of points; however, it is debatable...

problem is 1-dimensional – only the time dimension is relevant. The Maximum disjoint set problem is a generalization to 2 or more dimensions. This generalization...

estimation Quadtrees are also used in the area of fractal image analysis Maximum disjoint sets Quadtrees, particularly the region quadtree, have lent themselves...

filter Disjoint set Set (mathematics) For example, in Python pick can be implemented on a derived class of the built-in set as follows: class Set(set): def...

packing should be separable using only guillotine cuts. Maximum disjoint set (or Maximum independent set) is a problem in which both the sizes and the locations...

occurs if and only if A {\displaystyle A} and B {\displaystyle B} are disjoint sets. Furthermore, denoting D = A Δ B {\displaystyle D=A\mathbin {\Delta...

the independent set S {\displaystyle S} cannot be in S {\displaystyle S} because these vertices are disjoint by the independent set definition. If S...

says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices...

then it implies an O(1) approximation algorithm to the problem of maximum disjoint set of axes-parallel rectangles in time O ( n 5 ) {\displaystyle O(n^{5})}...

algorithms can use any of the algorithms for finding the maximum disjoint set from the set of potential labels. Other algorithms can also be used, like...

the vertices into disjoint dominating sets. The domatic number is the maximum size of a domatic partition. An eternal dominating set is a dynamic version...

we have to find the maximum number of edge-disjoint s-t paths in G. Menger's theorem states that the maximum number of edge-disjoint s-t paths in an undirected...

disjoint convex sets in n-dimensional Euclidean space. There are several rather similar versions. In one version of the theorem, if both these sets are...

four cap sets, the single point that when added to the 20 points of a cap set makes the entire sum go to 0 (mod 3). All cap sets in such a disjoint collection...

subset of an n {\displaystyle n} -element set, and an edge between every pair of disjoint sets. An independent set is a collection of vertices that has no...

partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset...

graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching...

members of X. Open balls of radius r centered at the points of X will all be disjoint from each other. The covering radius, R, of X is the smallest distance...

vertices. The domatic number is the maximum size of a domatic partition, that is, the maximum number of disjoint dominating sets. The graph in the figure has...

the ordering. A line graph is a graph whose edges can be covered by edge-disjoint cliques in such a way that each vertex belongs to exactly two of the cliques...