# Category: Spanning tree

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
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