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...

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...

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 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...

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

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...

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

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...

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...

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

edge-disjoint paths. Tuza's conjecture: if the maximum number of disjoint triangles is ν {\displaystyle \nu } , can all triangles be hit by a set of at...

P(α) = ∅. These theorems are proved by partitioning P′ into pairwise disjoint sets: P′ = (P′\ P(2)) ∪ (P(2) \ P(3)) ∪ ··· ∪ (P(∞) \ P(∞ + 1)) ∪ ··· ∪ P(α)...

the size of a minimum feedback vertex set is within a logarithmic factor of the maximum number of vertex-disjoint cycles in the given graph. Instead of...