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Least-weight tree connecting graph vertices
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all
Minimum_spanning_tree
In mathematics, a random minimum spanning tree may be formed by assigning independent random weights from some distribution to the edges of an undirected
Random_minimum_spanning_tree
Shortest network connecting points
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Tree which includes all vertices of a graph
graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of
Spanning_tree
rectilinear minimum spanning tree (RMST) of a set of n points in the plane (or more generally, in R d {\displaystyle \mathbb {R} ^{d}} ) is a minimum spanning tree
Rectilinear minimum spanning tree
Rectilinear_minimum_spanning_tree
Area of discrete mathematics
classification. Random minimal spanning tree is a spanning tree of a graph formed by choosing random edge weights and using the minimum spanning tree for those
Graph_theory
Index of articles associated with the same name
random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanning tree, a spanning tree of
Random_tree
Spanning tree type
Capacitated minimum spanning tree is a minimal cost spanning tree of a graph that has a designated root node r {\displaystyle r} and satisfies the capacity
Capacitated minimum spanning tree
Capacitated_minimum_spanning_tree
Kinetic data structure
A kinetic minimum spanning tree is a kinetic data structure that maintains the minimum spanning tree (MST) of a graph whose edge weights are changing as
Kinetic_minimum_spanning_tree
Graph generated by a random process
of tree components of order k is asymptotically Poisson. Types of random trees include uniform spanning tree, random minimum spanning tree, random binary
Random_graph
Minimum spanning forest algorithm that greedily adds edges
algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is a greedy
Kruskal's_algorithm
Topics referred to by the same term
k-minimum spanning tree Kinetic minimum spanning tree Random minimum spanning tree Rectilinear minimum spanning tree Degree-constrained spanning tree Maximum
Spanning tree (disambiguation)
Spanning_tree_(disambiguation)
In graph theory a minimum spanning tree (MST) T {\displaystyle T} of a graph G = ( V , E ) {\displaystyle G=(V,E)} with | V | = n {\displaystyle |V|=n}
Parallel algorithms for minimum spanning trees
Parallel_algorithms_for_minimum_spanning_trees
Method for finding minimum spanning trees
algorithm is a greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected
Borůvka's_algorithm
On short connecting nets with added points
tree problem in graphs is equivalent to the minimum spanning tree. However, while both the non-negative shortest path and the minimum spanning tree problem
Steiner_tree_problem
Method for finding minimum spanning trees
algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every
Prim's_algorithm
Sum of the inverses of the positive cubes
quantum electrodynamics. It also arises in the analysis of random minimum spanning trees and in conjunction with the gamma function when solving certain
Apéry's_constant
Binary tree derived from a sequence of numbers
minimax path weight in the minimum spanning tree of the metric. From the minimum spanning tree, one can construct a Cartesian tree, the root node of which
Cartesian_tree
The expected linear time MST algorithm is a randomized algorithm for computing the minimum spanning forest of a weighted graph with no isolated vertices
Expected linear time MST algorithm
Expected_linear_time_MST_algorithm
Graph with at most one cycle per component
augmented trees and maximal pseudoforests are also sometimes called augmented forests. The minimum spanning pseudoforest problem involves finding a spanning pseudoforest
Pseudoforest
Probability distribution on equally likely outcomes
simply, a random permutation is a permutation generated uniformly randomly from the permutations of a given set and a uniform spanning tree of a graph
Discrete_uniform_distribution
Automated methods for the creation of mazes
approached as generating a random spanning tree. Loops, which can confound naive maze solvers, may be introduced by adding random edges to the result during
Maze_generation_algorithm
British mathematician
probability theory including coalescent theory, random minimum spanning trees, and the theory of random graphs. She is professor of probability in the
Christina_Goldschmidt
This algorithm can only be applied to unweighted graphs. A minimum spanning tree is a tree-like subgraph of a given graph G, in which it keeps all the
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
Generalization of depth-first search trees
theory, a Trémaux tree of an undirected graph G {\displaystyle G} is a type of spanning tree, generalizing depth-first search trees. They are defined
Trémaux_tree
Randomized algorithm for minimum cuts
constructing the minimum spanning tree in a graph where the edges have weights w ( e i ) = π ( i ) {\displaystyle w(e_{i})=\pi (i)} according to a random permutation
Karger's_algorithm
Data structure for storing non-overlapping sets
in Kruskal's algorithm for finding the minimum spanning tree of a graph. The importance of minimum spanning trees means that disjoint-set data structures
Disjoint-set_data_structure
Classification of algorithm
implementation for an Expected Linear-Time Minimum Spanning Tree Algorithm(Karger-Klein-Tarjan + Hagerup Minimum Spanning Tree Verification as a sub-routine)".
Galactic_algorithm
Algorithm to search the nodes of a graph
conveniently described in terms of a spanning tree of the vertices reached during the search. Based on this spanning tree, the edges of the original graph
Depth-first_search
Subfield of mathematical optimization
optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems
Combinatorial_optimization
tree Ordered tree Recursive tree SPQR tree Suffix tree Technology tree Trie Patricia trie Spanning tree Minimum spanning tree Boruvka's algorithm Kruskal's
List_of_graph_theory_topics
Overview of and topical guide to algorithms
Floyd–Warshall algorithm Johnson's algorithm A* search algorithm Minimum spanning tree Kruskal's algorithm Prim's algorithm Borůvka's algorithm Connected
Outline_of_algorithms
Approximation for the travelling salesman problem
Removing an edge from C produces a spanning tree, which must have weight at least that of the minimum spanning tree, implying that w(T) ≤ w(C) - lower
Christofides_algorithm
Czech academic and mathematician
mathematically as a minimum spanning tree problem, and described the first known algorithm for finding the minimum spanning tree of a metric space (the
Otakar_Borůvka
American mathematician (1923–2013)
tree problem. This work also formulated the Gilbert–Pollak conjecture on the ratio between the length of the Steiner tree and minimum spanning tree.[GP68]
Edgar_Gilbert
French computer scientist (born 1955)
Discrepancy Method: Randomness and Complexity, Cambridge University Press, ISBN 978-0-521-00357-5 Chazelle, Bernard (2000), "A minimum spanning tree algorithm with
Bernard_Chazelle
Graph defined from a set of points in the Euclidean plane
given. The Gabriel graph contains, as subgraphs, the Euclidean minimum spanning tree, the relative neighborhood graph, and the nearest neighbor graph
Gabriel_graph
Smallest convex set containing a given set
finite set of points in three-dimensional space, a neighborhood of a spanning tree of the points encloses them with arbitrarily small surface area, smaller
Convex_hull
Python module
as graph isomorphism, subgraph isomorphism, minimum spanning tree, connected components, dominator tree, maximum flow, etc. Support for several centrality
Graph-tool
NP-hard problem in combinatorial optimization
For example, the minimum spanning tree of the graph associated with an instance of the Euclidean TSP is a Euclidean minimum spanning tree, and so can be
Travelling_salesman_problem
Computer science data structure
reduced by polynomial order. Examples of such problems are Prim's minimal-spanning-tree algorithm and Dijkstra's shortest-path algorithm. Priority queue: A
Heap_(data_structure)
Study of mathematical algorithms for optimization problems
maxima are defined similarly. While a local minimum is at least as good as any nearby elements, a global minimum is at least as good as every feasible element
Mathematical_optimization
Optimization algorithm
If other ants find such a path, they are likely to stop travelling at random and instead follow the trail, returning and reinforcing it if they eventually
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Farthest distance between two points
points Minimum-diameter spanning tree, a different notion of diameter for low-dimensional points based on the graph diameter of a spanning tree Toussaint
Diameter (computational geometry)
Diameter_(computational_geometry)
Maximal subgraph whose vertices can reach each other
algorithm for minimum spanning trees, which adds edges to a graph in sorted order by length and includes an edge in the minimum spanning tree only when it
Component_(graph_theory)
Optimization algorithm
versions of coordinate descent randomly pick a different coordinate direction each iteration.[citation needed] Random-restart hill climbing is a meta-algorithm
Hill_climbing
Data structure that maintains info about the connected components of a graph
contained in one of the spanning trees of FL. When such an edge e = x−y is deleted, it is first removed from FL and from all smaller spanning forests to which
Dynamic_connectivity
algorithm): find maximum or minimum branchings Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the
List_of_algorithms
Computing technique
is a basic technique in distributed algorithms. For instance, a (minimum) spanning tree is used as a backbone to reduce the cost of broadcast from O(m)
Topology_control
Model of computational complexity
bs(f)=O(s(f)^{4})} . Comparison sort Decision tree Aanderaa–Karp–Rosenberg conjecture Minimum spanning tree § Decision trees Ford, Lester R. Jr.; Johnson, Selmer
Decision_tree_model
Matroid with graph forests as independent sets
matroids are all isomorphic. A minimum weight basis of a graphic matroid is a minimum spanning tree (or minimum spanning forest, if the underlying graph
Graphic_matroid
Optimization algorithm
toward the local minimum. With this observation in mind, one starts with a guess x 0 {\displaystyle \mathbf {x} _{0}} for a local minimum of f {\displaystyle
Gradient_descent
American computer scientist
R.; Klein, P. N.; Tarjan, R. E. (1995). "A randomized linear-time algorithm to find minimum spanning trees". Journal of the ACM. 42 (2): 321. CiteSeerX 10
David_Karger
Statistical optimization technique
objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures beliefs about the
Bayesian_optimization
approximation. spanning A subgraph is spanning when it includes all of the vertices of the given graph. Important cases include spanning trees, spanning subgraphs
Glossary_of_graph_theory
Optimization algorithm
algorithm of choice" for fitting log-linear (MaxEnt) models and conditional random fields with ℓ 2 {\displaystyle \ell _{2}} -regularization. Since BFGS (and
Limited-memory_BFGS
Local search algorithm
improving move is available (like when the search is stuck at a strict local minimum). In addition, prohibitions (hence the term tabu) are introduced to discourage
Tabu_search
Quantum physics-based metaheuristic for optimization problems
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate
Quantum_annealing
Optimization technique
stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, there are many problems
Metaheuristic
Geometric graph connecting nearby points
subgraph of the Delaunay triangulation. In turn, the Euclidean minimum spanning tree is a subgraph of it, from which it follows that it is a connected
Relative_neighborhood_graph
Largest independent set of paired elements
boundary traced in this way. A Xuong tree is a spanning tree with the property that, in the subgraph of edges not in the tree, the number of connected components
Matroid_parity_problem
Edges that hit all cycles in a graph
minimum number of edges that need to be removed from a connected graph to reduce it to a spanning tree; it is much easier to compute than the minimum
Feedback_arc_set
Algorithm for linear programming
{b}}_{r}/{\hat {a}}_{rc}\,} is the minimum over all r such that a ^ r c {\displaystyle {\hat {a}}_{rc}} > 0. This is called the minimum ratio test. If there is more
Simplex_algorithm
Filtering Decision stumps (one-level decision trees) Density Estimation Trees Euclidean minimum spanning trees Gaussian Mixture Models (GMMs) Hidden Markov
Mlpack
Abstract data type in computer science
Using min heap priority queue in Prim's algorithm to find the minimum spanning tree of a connected and undirected graph, one can achieve a good running
Priority_queue
Network representing spatial objects
structure of edges it is useful to find the Minimum spanning tree, or the generalization, the Steiner tree and the relative neighborhood graph. In the
Spatial_network
Triangulation method
paired with a final iterative triangle flipping step. The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of
Delaunay_triangulation
Optimization algorithm
Yang and Deb discovered that the random-walk style search is better performed by Lévy flights rather than simple random walk. The pseudo-code can be summarized
Cuckoo_search
Form of Newton's method used in statistics
Ronald Fisher. Let Y 1 , … , Y n {\displaystyle Y_{1},\ldots ,Y_{n}} be random variables, independent and identically distributed with twice differentiable
Scoring_algorithm
Subfield of convex optimization
conditions by using an extended dual problem proposed by Ramana. Consider three random variables A {\displaystyle A} , B {\displaystyle B} , and C {\displaystyle
Semidefinite_programming
Theoretical model of computation
Michael L.; Willard, Dan E. (1994), "Trans-dichotomous algorithms for minimum spanning trees and shortest paths", Journal of Computer and System Sciences, 48
Transdichotomous_model
Method for mathematical optimization
and George J. Minty), in the worst case. However, when it is started at a random corner, the criss-cross algorithm on average visits only D additional corners
Criss-cross_algorithm
Points separated from others by a line
This parametric minimum spanning tree problem has been studied by various authors and can be used to solve other bicriterion spanning tree optimization problems
K-set_(geometry)
Mathematical algorithm
algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate
Coordinate_descent
Class of algorithms that find approximate solutions to optimization problems
on the metric. This is also known as metric embedding. Random sampling and the use of randomness in general in conjunction with the methods above. While
Approximation_algorithm
Population-based search algorithm
the environment looking for new flower patches. These scout bees move randomly in the area surrounding the hive, evaluating the profitability (net energy
Bees_algorithm
gradient descent Coordinate descent Frank–Wolfe algorithm Landweber iteration Random coordinate descent Conjugate gradient method Derivation of the conjugate
Gradient_method
Mapping arbitrary data to fixed-size values
that collide at the slot are added to the chain. Chains may be kept in random order and searched linearly, or in serial order, or as a self-ordering list
Hash_function
Collective behavior of decentralized, self-organized systems
dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of "intelligent"
Swarm_intelligence
Algorithm in computer science
{\displaystyle X_{j}} is a randomly selected candidate solution ( i ≠ j {\displaystyle i\neq j} ), k {\displaystyle k} is a random dimension index selected
Artificial bee colony algorithm
Artificial_bee_colony_algorithm
Unit hypercube of variable dimension whose corners have been perturbed
However according to Fukuda & Namiki (1994), when it is initialized at a random corner of the cube, the criss-cross algorithm visits only D {\displaystyle
Klee–Minty_cube
Vector quantization algorithm minimizing the sum of squared deviations
1007/s10994-009-5103-0. Dasgupta, S.; Freund, Y. (July 2009). "Random Projection Trees for Vector Quantization". IEEE Transactions on Information Theory
K-means_clustering
American and Canadian computer scientist
Klein, Philip N.; Tarjan, Robert E. (1995), "A randomized linear-time algorithm to find minimum spanning trees", Journal of the ACM, 42 (2): 321–328, doi:10
Valerie_King
Use of multiple antennas in radio
the radius constraint are visited. In the natural span scheme, the next node is selected randomly. Its advantage is that it avoids enumerating all possible
MIMO
algorithm out of the local minimum, through penalising features present in that local minimum. The idea is to make the local minimum more costly than the surrounding
Guided_local_search
Collective perception of a group of people
wisdom-of-the-crowds effects include: Combinatorial problems such as minimum spanning trees and the traveling salesman problem, in which participants must find
Wisdom_of_the_crowd
Variant on the simple heap data structure
been used to achieve the best complexity to date for finding a minimum spanning tree. Other problems whose efficient solution has been simplified using
Soft_heap
Mathematical algorithm for eliminating variables from a system of linear inequalities
{\displaystyle \mathbb {R} ^{2^{n}-1}} , where n {\displaystyle n} is the number of random variables appearing in the involved information measures. Consequently,
Fourier–Motzkin_elimination
underlying tree structure. In this view, the network consists of the skeleton and the shortcuts. The skeleton is a special type of spanning tree, formed
Fractal_dimension_on_networks
Python library for graphs and networks
Conversion of graphs to and from several formats. Ability to construct random graphs or construct them incrementally. Ability to find subgraphs, cliques
NetworkX
American computer scientist
In 1994, Klein and Robert E. Tarjan gave a randomized linear-time algorithm to find minimum spanning trees, based on a sampling technique due to David
Philip_N._Klein
Solving multiple machine learning tasks at the same time
(OMT) A general-purpose online multi-task learning toolkit based on conditional random field models and stochastic gradient descent training (C#, .NET)
Multi-task_learning
Optimization algorithm
fashion until the solution of the global system is found. The search for a minimum or maximum of a scalar-valued function is closely related to the search
Quasi-Newton_method
In evolutionary computation, Minimum Population Search (MPS) is a computational method that optimizes a problem by iteratively trying to improve a set
Minimum_Population_Search
Statistical method in data analysis
proximity matrix. For single linkage, optimized algorithms based on minimum spanning trees reduce the time complexity to O(n² log n). For other linkage criteria
Hierarchical_clustering
Algorithm for solving the quadratic programming problem from training SVMs
Vapnik. It is known as the "chunking algorithm". The algorithm starts with a random subset of the data, solves this problem, and iteratively adds examples which
Sequential minimal optimization
Sequential_minimal_optimization
Longest recorded life span
Maximum life span (or, for humans, maximum reported age at death) is a measure of the maximum amount of time one or more members of a population have been
Maximum_life_span
Method to solve optimization problems
function is a convex function, which implies that every local minimum is a global minimum; similarly, a linear function is a concave function, which implies
Linear_programming
Optimization algorithm
\mathbb {R} ^{n}} ( i = 1 , … , m ) {\displaystyle (i=1,\ldots ,m)} at random to satisfy the following condition: min i = 1 , … , m { max j = 1 , … ,
Spiral_optimization_algorithm
number of edges, and total weight close to that of the Euclidean minimum spanning tree. Although known construction methods for them are slow, fast approximation
Greedy_geometric_spanner
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
Surname or Lastname
English
English : variant of Ransom.
Boy/Male
English American
Son of Rand.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Boy/Male
English
Son of Rand.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Surname or Lastname
English
English : patronymic from Rand 1.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Surname or Lastname
English
English : variant of Brandon.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Surname or Lastname
English
English : unexplained. Perhaps a variant of Channon.The earliest American Channing was John, who came from Dorset, England, in 1711 with his wife. Their son John became a prosperous merchant of Newport, RI, and their grandson William Ellery was born there in 1780. William Ellery Channing (1780–1842) was a Unitarian clergyman who founded the Massachusetts Peace Society, a precursor of the modern anti-war movement.
Surname or Lastname
English and Scottish
English and Scottish : habitational name from a place in Lincolnshire, so called from the Old English tribal name Spaldingas ‘people of the district called Spald’. The district name probably means ‘ditches’, referring to drainage channels in the fenland.The surname was taken to Scotland in the 13th century by Radulphus de Spalding. His descendants prospered, and the name is still common in Scotland. Early American Spaldings include Thomas Spalding, born in Frederica, GA, in 1774, who introduced sea-island cotton in GA, and the physician Lyman Spalding, born in Cornish, NH, in 1775, who founded U.S. Pharmacopoeia.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
Boy/Male
American, British, English
Swift
Girl/Female
Indian
Angle; Gift of God
Male
Greek
(Αντώνιος) Greek name, possibly ANTONIOS means "invaluable."Â
Girl/Female
Arabic, Muslim
Glory of the Women
Boy/Male
Hindu, Indian
Nature
Boy/Male
Hindu, Indian, Punjabi, Sikh
Sweetness
Girl/Female
American, Australian, British, Christian, Danish, English, French, Greek, Hebrew, Swedish
Jehovah has been Gracious; Has Shown Favor; Noble; Female Version of John; The Lord is Gracious; Well-born
Girl/Female
English
Shining battlemaid.
Boy/Male
Hindu
Daring & dashing
Boy/Male
Indian, Punjabi, Sikh
Inner Love
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
RANDOM MINIMUM-SPANNING-TREE
n.
Random.
n.
Minimum.
a.
Not flowing; stagnant; as, standing water.
pl.
of Minimus
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
v. i.
To go or stray at random.
a.
Established by law, custom, or the like; settled; continually existing; permanent; not temporary; as, a standing army; legislative bodies have standing rules of proceeding and standing committees.
a.
Remaining erect; not cut down; as, standing corn.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
To exact a ransom for, or a payment on.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
adv.
In a random manner.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
pl.
of Minimum
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
n.
Condition in society; relative position; reputation; rank; as, a man of good standing, or of high standing.
n.
A minim.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.