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K-minimum spanning tree

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 of a larger graph. It is also called the

Spanning Tree Protocol

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 prevent bridge loops and the broadcast radiation

Spanning tree

In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may have several spannin

Grid bracing

In the mathematics of structural rigidity, grid bracing is a problem of adding cross bracing to a square grid to make it into a rigid structure. It can be solved optimally by translating it into a pro

Random minimum spanning tree

In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of

Xuong tree

In graph theory, a Xuong tree is a spanning tree of a given graph with the property that, in the remaining graph , the number of connected components with an odd number of edges is as small as possibl

Minimum bottleneck spanning tree

In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted

Net (polyhedron)

In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a

Expected linear time MST algorithm

The expected linear time MST algorithm is a randomized algorithm for computing the minimum spanning forest of a weighted graph with no isolated vertices. It was developed by David Karger, Philip Klein

Arboricity

The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to cover all the edges

Good spanning tree

In the mathematical field of graph theory, a good spanning tree of an embedded planar graph is a rooted spanning tree of whose non-tree edges satisfy the following conditions.
* there is no non-tree

Kirchhoff's theorem

In the mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that

Parallel algorithms for minimum spanning trees

In graph theory a minimum spanning tree (MST) of a graph with and is a tree subgraph of that contains all of its vertices and is of minimum weight. MSTs are useful and versatile tools utilised in a wi

Minimum routing cost spanning tree

In computer science, the minimum routing cost spanning tree of a weighted graph is a spanning tree minimizing the sum of pairwise distances between vertices in the tree. It is also called the optimum

Graphic matroid

In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the forests in a given finite undirected graph. The d

Borůvka's algorithm

Borůvka's 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. It was first published in 1926 by Ot

Minimum spanning tree

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 the vertices together, without any cycles and wi

Degree-constrained spanning tree

In graph theory, a degree-constrained spanning tree is a spanning tree where the maximum vertex degree is limited to a certain constant k. The degree-constrained spanning tree problem is to determine

Christofides algorithm

The Christofides algorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric spac

Capacitated minimum spanning tree

Capacitated minimum spanning tree is a minimal cost spanning tree of a graph that has a designated root node and satisfies the capacity constraint . The capacity constraint ensures that all subtrees (

Reverse-delete algorithm

The reverse-delete algorithm is an algorithm in graph theory used to obtain a minimum spanning tree from a given connected, edge-weighted graph. It first appeared in , but it should not be confused wi

Tree spanner

A tree k-spanner (or simply k-spanner) of a graph is a spanning subtree of in which the distance between every pair of vertices is at most times their distance in .

Circuit rank

In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break

Prim's algorithm

In computer science, Prim's algorithm (also known as Jarník's algorithm) is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the e

Bridge protocol data unit

Bridge Protocol Data Units (BPDUs) are frames that contain information about the spanning tree protocol (STP). A switch sends BPDUs using a unique source MAC address from its origin port to a multicas

Shortest-path tree

In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex

Multiple Spanning Tree Protocol

The Multiple Spanning Tree Protocol (MSTP) and algorithm, provides both simple and full connectivity assigned to any given Virtual LAN (VLAN) throughout a Bridged Local Area Network. MSTP uses BPDUs t

Distributed 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 nodes communicate by message passing. It is radi

Minimum degree spanning tree

In graph theory, a minimum degree spanning tree is a subset of the edges of a connected graph that connects all the vertices together, without any cycles, and its maximum degree of its vertices as sma

Markov chain tree theorem

In the mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many states. It sums up terms for the rooted

Minimum spanning tree-based segmentation

Image segmentation strives to partition a digital image into regions of pixels with similar properties, e.g. homogeneity. The higher-level region representation simplifies image analysis tasks such as

Uniform spanning tree

No description available.

Virtual Link Trunking

Virtual Link Trunking (VLT) is a name that has been used for at least two proprietary network protocols. A link aggregation protocol developed by Force10 and an early VLAN tagging capability from 3Com

Trémaux tree

In graph theory, a Trémaux tree of an undirected graph is a type of spanning tree, generalizing depth-first search trees.They are defined by the property that every edge of connects an ancestor–descen

Rectilinear minimum spanning tree

In graph theory, the rectilinear minimum spanning tree (RMST) of a set of n points in the plane (or more generally, in ℝd) is a minimum spanning tree of that set, where the weight of the edge between

Euclidean minimum spanning tree

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 of line segments with the points as endpoints,

Kinetic minimum spanning tree

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 a continuous function of time.

Kruskal's algorithm

Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. (A minimum spanning tree of a connected graph is

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