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Least-weight tree connecting graph vertices
In graph theory, a minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph
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
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
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
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
weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck
Minimum bottleneck spanning tree
Minimum_bottleneck_spanning_tree
Minimum-cost tree with exactly k vertices
The k-minimum spanning tree problem, studied in theoretical computer science, asks for a tree of minimum cost that has exactly k vertices and forms a subgraph
K-minimum_spanning_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
The distributed minimum spanning tree (MST) problem involves the construction of a minimum spanning tree by a distributed algorithm, in a network where
Distributed minimum spanning tree
Distributed_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
are computed as the difference of pixel intensities. A minimum spanning tree (MST) is a minimum-weight, cycle-free subset of a graph's edges such that
Minimum spanning tree-based segmentation
Minimum_spanning_tree-based_segmentation
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
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
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
A kinetic Euclidean minimum spanning tree is a kinetic data structure that maintains the Euclidean minimum spanning tree (EMST) of a set P of n points
Kinetic Euclidean minimum spanning tree
Kinetic_Euclidean_minimum_spanning_tree
Tree connecting given points by short paths
and computational geometry, a minimum-diameter spanning tree of a finite set of points in a metric space is a spanning tree in which the diameter (the longest
Minimum-diameter spanning tree
Minimum-diameter_spanning_tree
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
Network protocol that builds a loop-free logical topology for Ethernet networks
The Spanning Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to
Spanning_Tree_Protocol
Graph theory concept
This is also known as the degree-constrained spanning tree problem. Finding the minimum degree spanning tree of an undirected graph is NP-hard. This can
Minimum_degree_spanning_tree
they need to construct a spanning tree. Each edge in the graph has a cost, and the players build the minimum cost spanning tree. The question then arises
Minimum-cost spanning tree game
Minimum-cost_spanning_tree_game
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
Spanning tree minimizing sum of distances
distance spanning tree, shortest total path length spanning tree, minimum total distance spanning tree, or minimum average distance spanning tree. In an
Minimum routing cost spanning tree
Minimum_routing_cost_spanning_tree
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
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
Algorithm for the directed version of the minimum spanning tree problem
finding a spanning arborescence of minimum weight (sometimes called an optimum branching). It is the directed analog of the minimum spanning tree problem
Edmonds'_algorithm
Network protocol that builds a loop-free logical topology for Ethernet networks
Wikimedia Commons has media related to Multiple Spanning Tree Protocol. The Multiple Spanning Tree Protocol (MSTP) and algorithm, provides both simple
Multiple Spanning Tree Protocol
Multiple_Spanning_Tree_Protocol
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
Unsolved problem in graph theory
unproven conjecture on the ratio of lengths of Steiner trees and Euclidean minimum spanning trees for the same point sets in the Euclidean plane. It was
Gilbert–Pollak_conjecture
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
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
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
Sequence of locally optimal choices
algorithm and Prim's algorithm are greedy algorithms for constructing minimum spanning trees of a given connected graph. They always find an optimal solution
Greedy_algorithm
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
Type of spanning tree
of degree-confined spanning tree is the Hamiltonian path problem. On a weighted graph, a Degree-constrained minimum spanning tree (DCMST) is a degree-constrained
Degree-constrained spanning tree
Degree-constrained_spanning_tree
topological minors Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. (The minimum spanning tree for an entire graph is solvable
List_of_NP-complete_problems
Area of discrete mathematics
selected. Being a spanning tree means that a subgraph is a tree that includes all of the vertices of a graph. The uniform spanning tree can be generated
Graph_theory
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
Index of articles associated with the same name
and using the minimum spanning tree for those weights Random binary tree, binary trees with various random distributions, including trees formed by random
Random_tree
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
Topics referred to by the same term
containing spanning tree Minimum spanning tree Capacitated minimum spanning tree Distributed minimum spanning tree Euclidean minimum spanning tree k-minimum spanning
Spanning tree (disambiguation)
Spanning_tree_(disambiguation)
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 by removing non-optimal solutions to subproblems
is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution
Branch_and_bound
the minimum spanning tree of G by the cycle property. Given a forest, F-heavy edges can be computed in linear time using a minimum spanning tree verification
Expected linear time MST algorithm
Expected_linear_time_MST_algorithm
Sequential model-based optimization of expensive black-box functions
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Bayesian_optimization
endpoints of the network edges, then the shortest network is their minimum spanning tree. However, shorter networks can often be obtained by adding Steiner
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
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
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
Algorithm used to solve non-linear least squares problems
optimization algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum. The primary application of the Levenberg–Marquardt
Levenberg–Marquardt_algorithm
Length of a line segment
called the squared Euclidean distance. For instance, the Euclidean minimum spanning tree can be determined using only the ordering between distances, and
Euclidean_distance
Problem optimization method
that holds the minimum value at each rank gives us the shortest path between rank n and rank 1. The function q(i, j) is equal to the minimum cost to get
Dynamic_programming
Mathematical optimization problem restricted to integers
{\displaystyle d} of A {\displaystyle A} is the minimum of the tree-depth of the graph of A {\displaystyle A} and the tree-depth of the graph of the transpose of
Integer_programming
Optimization algorithm
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Limited-memory_BFGS
Data structures used to track continuously moving geometric bodies
Kinetic convex hull Kinetic closest pair Kinetic minimum spanning tree Kinetic Euclidean minimum spanning tree Kinetic Yao graph Kinetic Semi-Yao graph (a
Kinetic_data_structure
Methods in numerical computation
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Rosenbrock_methods
Path-finding using high-weight graph edges
the maximum spanning tree of the graph, and a minimax path may be found as the path between the two vertices in the minimum spanning tree. It follows
Widest_path_problem
Subgraph of Delaunay triangulation
graph of a set of points in general position contains the Euclidean minimum spanning tree of its points, from which it follows that it is a connected graph
Urquhart_graph
Optimizing objective functions that have constrained variables
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Constrained_optimization
Algorithm for finding shortest paths
greedy process used in Prim's algorithm. Prim's purpose is to find a minimum spanning tree that connects all nodes in the graph; Dijkstra is concerned with
Dijkstra's_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)
Minimum spanning forest algorithm that greedily deletes edges
will find a minimum spanning tree for each disconnected part of the graph. The set of these minimum spanning trees is called a minimum spanning forest, which
Reverse-delete_algorithm
Subfield of mathematical optimization
of convex optimization problems: every point that is local minimum is also a global minimum; the optimal set is convex; if the objective function is strictly
Convex_optimization
Algorithm for finding zeros of functions
Newton's method can be used to find a minimum or maximum of a function f(x). The derivative is zero at a minimum or maximum, so local minima and maxima
Newton's_method
Optimization technique
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Metaheuristic
Solution process for some optimization problems
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Nonlinear_programming
Set of all Pareto efficient situations
Amadeu A. (September 2023). "On solving bi-objective constrained minimum spanning tree problems". Journal of Global Optimization. 87 (1): 301–323. doi:10
Pareto_frontier
Numerical optimization algorithm
method, or polytope method) is a numerical method used to find a local minimum or maximum of an objective function in a multidimensional space. It is
Nelder–Mead_method
French computer scientist (born 1955)
asymptotically efficient known deterministic algorithm for finding minimum spanning trees. Chazelle was born in Clamart, France, the son of Marie-Claire (née
Bernard_Chazelle
Algorithms for solving convex optimization problems
\cdot t_{i}} . For each ti, we find an approximate minimum of fti, denoted by xi. The approximate minimum is chosen to satisfy the following "closeness condition"
Interior-point_method
Computational technique
build the trajectory Monocle computes a minimum spanning tree, then finds the longest connected path in that tree. Cells are projected onto the nearest
Trajectory_inference
Data structure
"Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity". Journal of the ACM. 48 (4): 723. doi:10
Top_tree
Numerical approximation algorithm
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Iterative_method
Collective behavior of decentralized, self-organized systems
case had. One such instance is Ant-inspired Monte Carlo algorithm for Minimum Feedback Arc Set where this has been achieved probabilistically via hybridization
Swarm_intelligence
Inequalities for inexact line search
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Wolfe_conditions
Agglomerative hierarchical clustering method
minimum spanning trees. However, in single linkage clustering, the order in which clusters are formed is important, while for minimum spanning trees what
Single-linkage_clustering
PFNet(n-1,\infty )} will be the minimum spanning tree for the links defined by the proximity data if a unique minimum spanning tree exists. In general, the P
Pathfinder_network
Solving an optimization problem with a quadratic objective function
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Quadratic_programming
Method of solving linear programming problems
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Big_M_method
Topics referred to by the same term
Prim, abbreviation for Primitive Methodist Prim's algorithm for minimum spanning tree, developed by Robert C. Prim PRIM (watches), a Czech trademark Graham
Prim
Type of algorithm for constrained optimization
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Penalty_method
Variant of the Steiner tree problem in geometry and combinatorics
algorithms exist which start from the rectilinear minimum spanning tree (RMST; the minimum spanning tree in the plane with rectilinear distance) and try
Rectilinear_Steiner_tree
Topics referred to by the same term
help others learn about Microsoft technology Microsoft Surface Pro Minimum spanning tree, a graph theory problem MSP (file format), a pre-bmp picture format
MSP
Optimization method
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Technique for finding an extremum of a function
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal
Golden-section_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
Population-based search algorithm
variables min = [..] ; % an array of the size maxParameters to indicate the minimum value of each input parameter max = [..] ; % an array of the size maxParameters
Bees_algorithm
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
Class of algorithms that find approximate solutions to optimization problems
polynomial-time algorithm that uses at most one additional color than the minimum needed. A notable example of an approximation algorithm that provides both
Approximation_algorithm
Optimization algorithm
optimization, line search is a basic iterative approach to find a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f : R n →
Line_search
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Gradient_method
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
Mathematical combinatorial optimization method
and price is a branch and bound method in which at each node of the search tree, columns may be added to the linear programming relaxation (LP relaxation)
Branch_and_price
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
Canadian mathematician and computer scientist
complexity of H-coloring" also with Nešetřil, "On the history of the minimum spanning tree problem", with Ron Graham, "On the completeness of a generalized
Pavol_Hell
Mathematical algorithm for eliminating variables from a system of linear inequalities
inequalities based solely on syntactic properties of the formula derivation tree, thus curtailing the need to solve linear programs or compute matrix ranks
Fourier–Motzkin_elimination
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
Form of Newton's method used in statistics
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Scoring_algorithm
Class of algorithms for solving constrained optimization problems
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Augmented_Lagrangian_method
Optimization algorithm
Partition problem (SPP) Weight constrained graph tree partition problem (WCGTPP) Arc-weighted l-cardinality tree problem (AWlCTP) Multiple knapsack problem
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Optimization technique for solving (mixed) integer linear programs
algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning tree Borůvka Prim Kruskal Shortest path Bellman–Ford SPFA Dijkstra Floyd–Warshall
Cutting-plane_method
Algorithm for solving the quadratic programming problem from training SVMs
and this reduced problem can be solved analytically: one needs to find a minimum of a one-dimensional quadratic function. k {\displaystyle k} is the negative
Sequential minimal optimization
Sequential_minimal_optimization
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MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
MINIMUM SPANNING-TREE
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