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Data structure for storing non-overlapping sets
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)
Disjoint-set_data_structure
Sets with no element in common
set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are
Disjoint_sets
Data organization and storage formats
b)-tree Link/cut tree SPQR-tree Spaghetti stack Disjoint-set data structure (Union-find data structure) Fusion tree Enfilade Exponential tree Fenwick tree
List_of_data_structures
Abstract data type for storing distinct values
in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed. Static sets allow only query
Set_(abstract_data_type)
Minimum spanning forest algorithm that greedily adds edges
The key steps of the algorithm are sorting and the use of a disjoint-set data structure to detect cycles. Its running time is dominated by the time to
Kruskal's_algorithm
In mathematics, operation on sets
In mathematics, the disjoint union (or discriminated union) A ⊔ B {\displaystyle A\sqcup B} of the sets A and B is the set formed from the elements of
Disjoint_union
Basic concept of graph theory
computationally whether a graph is connected (for example, by using a disjoint-set data structure), or to count the number of connected components. A simple algorithm
Connectivity_(graph_theory)
{\displaystyle \delta =o(b)} bits). In the disjoint-set data structure, the structure represents a collection of disjoint sets; there is an update operation, called
Cell-probe_model
Mathematical model for data types
possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete
Abstract_data_type
Topics referred to by the same term
both being true Disjoint union Disjoint-set data structure This disambiguation page lists articles associated with the title Disjoint. If an internal
Disjoint
algorithm's access to the structure vary. This model has been used extensively with problems related to the disjoint-set data structure. Thus, Tarjan and La
Pointer_algorithm
Way of storing data in a computer
In computer science, a linked data structure is a data structure which consists of a set of data records (nodes) linked together and organized by references
Linked_data_structure
Quickly growing function
appears in the time complexity of some algorithms, such as the disjoint-set data structure and Chazelle's algorithm for minimum spanning trees. Sometimes
Ackermann_function
Proof assistant
language which is largely programmed and proven correct in Rocq. Disjoint-set data structure: correctness proof in Rocq was published in 2007. Feit–Thompson
Rocq
Tree representation of the abstract syntactic structure of source code
An abstract syntax tree (AST) is a data structure used in computer science to represent the structure of a program or code snippet. It is a tree representation
Abstract_syntax_tree
Partition of an interval Partition of a set Ordered partition Partition refinement Disjoint-set data structure Partition problem 3-partition problem Partition
List_of_partition_topics
Tree data structure
also used as disjoint-set data structures. The structure can be regarded as a set of singly linked lists that share part of their structure, in particular
Parent_pointer_tree
Describes approximate behavior of a function
Algorithms and Data Structures. U.S. National Institute of Standards and Technology. Retrieved December 16, 2006. The Wikibook Data Structures has a page
Big_O_notation
to the union-find data structure, which also maintains a partition into disjoint sets but in which the operations merge pairs of sets. In some applications
Partition_refinement
Automated methods for the creation of mazes
efficient implementation using a disjoint-set data structure can perform each union and find operation on two sets in nearly constant amortized time
Maze_generation_algorithm
Linked node hierarchical data structure
science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree
Tree_(abstract_data_type)
Declarative logic programming language
of data structures used to store relations; common choices include hash tables and B-trees, other possibilities include disjoint set data structures (for
Datalog
Abstract data type
counter to keep track of the size of the list: structure frame: data : item next : frame or nil structure stack: head : frame or nil size : integer procedure
Stack_(abstract_data_type)
American computer scientist and mathematician
Sleator). Another significant contribution was the analysis of the disjoint-set data structure; he was the first to prove the optimal runtime involving the
Robert_Tarjan
Attribute of data
about (disjoint) unions or Cartesian products of types. Value space and behaviour A type is a set of values which a variable can possess and a set of functions
Data_type
Maximal subgraph whose vertices can reach each other
components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly
Component_(graph_theory)
Data type defined by combining other types
are known as tagged unions or disjoint unions. Each variant has a name, called a constructor, which can also carry data. Enumerated types are a simple
Algebraic_data_type
On short connecting nets with added points
one tree remains. By using a Heap (data structure) to implement the priority queue and a disjoint-set data structure to track to which tree each visited
Steiner_tree_problem
Sets whose elements have degrees of membership
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
Fuzzy_set
Branch of mathematics that studies sets
relationships between them, treating sets as one particular kind of structure within this broader framework. From set theory's inception, some mathematicians
Set_theory
Algorithmic application of graph theory
a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l)
Connected-component_labeling
Set of elements common to all of some sets
disjoint, while the set of even numbers intersects the set of multiples of 3 at the multiples of 6. two parallel lines in the same plane are disjoint
Intersection_(set_theory)
Maximal biconnected subgraph
developed an efficient data structure for this problem based on disjoint-set data structures. Specifically, it processes n vertex additions and m edge additions
Biconnected_component
Data structure
In computer science, the log-structured merge-tree (also known as LSM tree, or LSMT) is a data structure with performance characteristics that make it
Log-structured_merge-tree
Parts of a whole which carry only relative information
In probability and statistics, a partition of the sampling space into disjoint events is described by the probabilities assigned to such events. The vector
Compositional_data
Detecting cycles is possible in near-constant time with the aid of a disjoint-set data structure. Pixel similarity is judged by a heuristic, which compares the
Minimum spanning tree-based segmentation
Minimum_spanning_tree-based_segmentation
Topics referred to by the same term
computer science programming idiom Disjoint-set data structure, a data structure used to track disjoint sets Distress signal unit, used by firefighters Dynamic
DSU
Data type that refers to itself in its definition
in computer science is in defining dynamic data structures such as Lists and Trees. Recursive data structures can dynamically grow to an arbitrarily large
Recursive_data_type
Overview of and topical guide to algorithms
Trie Segment tree Fenwick tree Heap (data structure) Hash table Hash function Bloom filter Disjoint-set data structure Union–find algorithm Locality-sensitive
Outline_of_algorithms
Search tree data structure
prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in
Trie
Unrelated vertices in graphs
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
Independent set (graph theory)
Independent_set_(graph_theory)
Algorithm in graph theory
adjacency structure in the paper). For reference, here are optimized versions of MakeSet, Find, and Union for a disjoint-set forest: function MakeSet(x) is
Tarjan's off-line lowest common ancestors algorithm
Tarjan's_off-line_lowest_common_ancestors_algorithm
Order whose elements are all comparable
the structure ( A i , ≤ i ) {\displaystyle (A_{i},\leq _{i})} is a linear order, where the sets A i {\displaystyle A_{i}} are pairwise disjoint, then
Total_order
Family of problems in computational geometry
cases exist. The problem may be stated for a set of arbitrary regions in space, not necessarily disjoint and not necessarily constituting a partition
Point_location
Data structure that maintains info about the connected components of a graph
a disjoint-set data structure. Each set represents a connected component; there is a path between x and y if and only if they belong to the same set. The
Dynamic_connectivity
Data type that represents an ordered collection of elements (values or variables)
The second axiom means that elements with distinct indices behave as disjoint variables, so that storing a value in one element does not affect the value
Array_(data_type)
Approximation of a mathematical set
rough set theory, the notion of dependency is defined very simply. Let us take two (disjoint) sets of attributes, set P {\displaystyle P} and set Q {\displaystyle
Rough_set
Architectural pattern in computer software development
(relatively) static data model with relations. The data design is usually coded up as conventional classes that represent the basic domain structure of the system
Data,_context_and_interaction
Method for partitioning partial orders into levels
the algorithm efficiently by using a disjoint-set data structure. In particular, with a version of this structure published later by Gabow & Tarjan (1985)
Coffman–Graham_algorithm
Constructs a fiber bundle from a base space, fiber and a set of transition functions
which constructs a fiber bundle with a structure group from a given base space, fiber, group, and a suitable set of transition functions. The theorem also
Fiber bundle construction theorem
Fiber_bundle_construction_theorem
Edges that hit all cycles in a graph
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
Feedback_arc_set
Finite sets whose elements are all hereditarily finite sets
mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself
Hereditarily_finite_set
Mathematical set with an ordering
composition is the disjoint union of two partially ordered sets, with no order relation between elements of one set and elements of the other set. The examples
Partially_ordered_set
Union data structure with enforced cases
variant record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value that could take on several
Tagged_union
Axiomatic set theories based on the principles of mathematical constructivism
rarely used in classical mathematics. Two ways to express that classes are disjoint does capture many of the intuitionistically valid negation rules: ( ∀ (
Constructive_set_theory
divides the data, S, into ℓ pieces, clusters each one of them (using k-means) and then clusters the centers obtained. Divide S into ℓ disjoint pieces X 1
Data_stream_clustering
Independent set which is not a subset of any other independent set
the independent set S {\displaystyle S} cannot be in S {\displaystyle S} because these vertices are disjoint by the independent set definition. If S
Maximal_independent_set
Elements in exactly one of two sets
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
Symmetric_difference
Abstraction of disjoint paths in directed graphs
gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint paths in a directed graph. The concept of a gammoid
Gammoid
Tree data structure that partitions a 2D area
A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are
Quadtree
supporting the find and union operations only. It can be solved by a disjoint-set data structure in O ( α ( n ) ) {\displaystyle O(\alpha (n))} amortized time
Interval_union-split-find
Field of study in artificial intelligence
training data and workflows, SISA reduces the computational burden of unlearning requests. Sharding divides the training dataset into multiple disjoint subsets
Machine_unlearning
Tree data structure with a variable and unbounded number of branches per node
tree if either T = {x} for some data point x or T = {T1, ... ,TnT} where Ti's are rose trees over disjoint sets of data points. Bird, Richard (1998). Introduction
Rose_tree
Adjacent subset of an undirected graph
expression data as one of finding the minimum number of changes needed to transform a graph describing the data into a graph formed as the disjoint union of
Clique_(graph_theory)
Number in {..., –2, –1, 0, 1, 2, ...}
{\displaystyle P} . Then construct a set P − {\displaystyle P^{-}} which is disjoint from P {\displaystyle P} and in one-to-one correspondence with P
Integer
Data type in type theory
algebraic data types. Just as product types and sum types are analogous to the cartesian product and disjoint union of abstract algebraic structures, quotient
Quotient_type
Space partitioning data structure
be searched. Each internal node of the tree partitions the data points into two disjoint sets which are associated with different balls. While the balls
Ball_tree
American computer scientist (born 1942)
matching. Already during his years at Michigan, Fischer studied disjoint-set data structures together with Bernard Galler. Fischer is one of the pioneers
Michael_J._Fischer
Division of an entire space into ≥2 disjoint subsets
space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space
Space_partitioning
Bound on eigenvalues
other two radii) covers all three eigenvalues. If one of the discs is disjoint from the others then it contains exactly one eigenvalue. If however it
Gershgorin_circle_theorem
Data type that allows for values that are one of multiple different data types
or a variable that may hold such a data structure. Some programming languages support a union type for such a data type. In other words, a union type
Union_type
Method for speeding related binary searches
sequence of binary searches for the same value in a sequence of related data structures. The first binary search in the sequence takes a logarithmic amount
Fractional_cascading
Foundations of probability theory
This is the assumption of σ-additivity: Any countable sequence of disjoint sets (synonymous with mutually exclusive events) E 1 , E 2 , … {\displaystyle
Probability_axioms
Node ordering for directed acyclic graphs
resulting sort, the structure S can be simply a set or a queue or a stack. Depending on the order that nodes n are removed from set S, a different solution
Topological_sorting
Problem in computer science
one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words
Set_packing
Tendency of a processor to access nearby memory locations in space or time
circumstances to accept, depending on the aspect. The reasons below are not disjoint; in fact, the list below goes from the most general case to special cases:
Locality_of_reference
Basic subset of a topological space
a countable union of disjoint open intervals. A set might be open, closed, both, or neither. In particular, open and closed sets are not mutually exclusive
Open_set
Element mapped to itself by a mathematical function
f(c) = c. In particular, f cannot have any fixed point if its domain is disjoint from its codomain. If f is defined on the real numbers, it corresponds
Fixed_point_(mathematics)
Extension of the Web to facilitate data exchange
Wide Web through standards set by the World Wide Web Consortium (W3C). The goal of the Semantic Web is to make Internet data machine-readable. To enable
Semantic_Web
Description of non-logical symbols
S_{\operatorname {func} }} and S rel {\displaystyle S_{\operatorname {rel} }} are disjoint sets not containing any other basic logical symbols, called respectively
Signature_(logic)
Computational problem in graph theory
iff there are k {\displaystyle k} edge-disjoint paths. 2. The paths must be independent, i.e., vertex-disjoint (except for s {\displaystyle s} and t {\displaystyle
Maximum_flow_problem
Computing problem
be handled accordingly so that all of these subpaths are disjoint and from all of them a set of O ( 1 / τ ) {\displaystyle O(1/\tau )} candidates is derived
Range query (computer science)
Range_query_(computer_science)
Function type in category theory
Now use the coproduct (the disjoint union of sets) to glue the three morphisms in one: α = e + i + m {\displaystyle
F-algebra
Data structure for integer priorities
A bucket queue is a data structure that implements the priority queue abstract data type: it maintains a dynamic collection of elements with numerical
Bucket_queue
Vertices connected in pairs by edges
discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense
Graph_(discrete_mathematics)
Design of geospatial data storage
nature of spatial information has led to its own set of model structures, much of the process of data modeling is similar to the rest of information technology
Data_model_(GIS)
Data structure
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and
Fenwick_tree
Undirected, connected, and acyclic graph
one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A directed tree, oriented tree, polytree, or singly connected
Tree_(graph_theory)
Field of mathematics which studies incidence structures
properties are considered. An incidence structure (P, L, I) consists of a set P whose elements are called points, a disjoint set L whose elements are called lines
Incidence_geometry
Mathematical ranking of a set
of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another
Weak_ordering
Graphical model
parameterize from data, as there are efficient algorithms for learning both the structure and probabilities of a dependency network from data. Such algorithms
Dependency network (graphical model)
Dependency_network_(graphical_model)
3. Sometimes used instead of ⊔ {\displaystyle \sqcup } for a disjoint union of sets. − (minus sign) 1. Denotes subtraction and is read as minus;
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Mathematical structure
X\mapsto X\sqcup \{*\}:\mathbf {Set} \to \mathbf {Set} } that sends a set to its disjoint union with the singleton set { ∗ } {\displaystyle \{\ast \}}
F-coalgebra
Operation in algebra and mathematics
or partiality monad adds a disjoint point: ( − ) ∗ : S e t → S e t {\displaystyle (-)_{*}:\mathbf {Set} \to \mathbf {Set} } X ↦ X ∪ { ∗ } {\displaystyle
Monad_(category_theory)
Cryptographic attack
t {\displaystyle t} points. Those two sets of m t {\displaystyle mt} and t {\displaystyle t} points are disjoint by the birthday paradox if we make sure
Time/memory/data tradeoff attack
Time/memory/data_tradeoff_attack
Vertices whose removal breaks all cycles
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
Feedback_vertex_set
Partition of a graph by removing fewest possible edges
min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. In the simplest unweighted min-cut
Minimum_cut
Branch of mathematics
definition.) The disjoint union of two posets is another typical example of order construction, where the order is just the (disjoint) union of the original
Order_theory
Economic model of personal preferences
both w>x and y>z. There are even distributions with disjoint supports, which induce the same set of choice probabilities. Some conditions for uniqueness
Random_utility_model
Inter-process communication API
(in ISO terminology, the TSAPs), is completely disjoint from that of TCP ports. An application may set up a UDP server on port number 7654 as follows
Berkeley_sockets
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
Female
Polish
 Variant spelling of Polish Dyta, DITA means "rich battle." Compare with another form of Dita.
Female
Hungarian
 Short form of Hungarian Katalin, KATA means "pure." Compare with other forms of Kata.
Female
English
 English surname transferred to unisex forename use, possibly DANA means "from Denmark." Compare with other forms of Dana.
Female
Finnish
Variant form of Finnish Aada, AATA means "noble."
Female
Hindi/Indian
(लता) Hindi name derived from a plant name, from the Sanskrit word lata, LATA means "creeper," in reference to a creeping plant.
Female
Egyptian
, an uncertain goddess.
Female
Russian
 Short form of Russian Yekaterina, KATA means "pure." Compare with other forms of Kata.
Female
Slavic
 Short form of Slavic Bogdana, DANA means "gift from God." Compare with other forms of Dana.
Male
Turkish
Turkish name ATA means "ancestor."
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Male
Irish
 From Irish Gaelic Mac Dara, DARA means "son of oak." Compare with other forms of Dara.
Female
Hebrew
(×“Ö¼Ö¸× Ö¸×”) Feminine form of Hebrew Dan, DANA means "judge." Compare with other forms of Dana.
Male
Hebrew
(דֶּרַע) Hebrew name DARA means "the arm." In the bible, this is the name of a son of Zerah. Compare with other forms of Dara.
Male
Hebrew
Variant spelling of Hebrew Dathan, DATAN means "belonging to a fountain."
Male
Iranian/Persian
 Short form of Persian Dârayavahush, DARA means "possesses a lot, wealthy." Compare with other forms of Dara.
Male
English
English surname transferred to unisex forename use, possibly DANA means "from Denmark."
Female
English
 Middle English name DARA means "brave, daring." Compare with another form of Dara.
Female
Polish
Short form of Polish Edyta, DYTA means "rich battle."
Female
Hebrew
(דִּיתָה) Pet form of Hebrew Yehuwdiyth, DITA means "Jewess" or "praised." Compare with another form of Dita.
Female
Finnish
 Short form of Finnish Katariina, KATA means "pure." Compare with other forms of Kata.
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
Boy/Male
Hindu
Offering to God during Pooja
Boy/Male
Assamese, Bengali, Hindu, Indian, Kannada, Marathi, Telugu
Quiet
Boy/Male
Tamil
Sudharsan | ஸà¯à®¤à®¾à®°à¯à®¸à®¨Â
Lord Perumal, Good looking, Lion, Vishnus weapon
Boy/Male
Tamil
Agasthya | அகஸà¯à®¤à¯à®¯
A name of a sage
Female
English
Feminine form of Greek Nereus, NERINE means "daughter of Nereus" or "sea sprite" or "wet one." It is also the name of a genus of plants native to South Africa but now spread worldwide. It is a bulb plant that produces beautiful pink funnel-shaped flowers in the fall, similar to the Belladonna Lily, though smaller. In use by the English.
Female
Czechoslovakian
, pearl.
Female
Finnish
Finnish form of Norwegian/Swedish Viva, VIIVA means "alive; animated; lively."
Girl/Female
Latin
Industrious; striving.
Boy/Male
Gaelic
Wealthy or stubborn.
Girl/Female
Tamil
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
DISJOINT SET-DATA-STRUCTURE
v.
To lend money upon, deducting the discount or allowance for interest; as, the banks discount notes and bills of exchange.
v. t.
To disjoin.
n.
The fruit of the date palm; also, the date palm itself.
imp. & p. p.
of Disjoin
p. pr. & vb. n.
of Disjoin
v. t.
To separate the joints of; to separate, as parts united by joints; to put out of joint; to force out of its socket; to dislocate; as, to disjoint limbs; to disjoint bones; to disjoint a fowl in carving.
imp. & p. p.
of Disjoint
v. t.
To break the natural order and relations of; to make incoherent; as, a disjointed speech.
v. t.
To disjoint.
v. t.
To discount. See Discount.
v. t.
To invalidate the consecration of; as, to disanoint a king.
v. t.
To disjoint.
v. t.
To disjoint; to separate.
v. t.
To separate at junctures or joints; to break where parts are united; to break in pieces; as, disjointed columns; to disjoint and edifice.
v. t.
To note or fix the time of, as of an event; to give the date of; as, to date the building of the pyramids.
adv.
In a disjointed state.
a.
Disjointed; unconnected; -- opposed to conjoint.
n. pl.
See Datum.
p. pr. & vb. n.
of Disjoint
v. i.
To lend, or make a practice of lending, money, abating the discount; as, the discount for sixty or ninety days.