신장 트리

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Pythagoras0 (토론 | 기여)님의 2020년 12월 26일 (토) 06:15 판 (→‎메타데이터: 새 문단)
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노트

  • For instance in the example above, twelve of sixteen spanning trees are actually paths.[1]
  • A spanning tree in G is a subgraph of G that includes all the vertices of G and is also a tree.[2]
  • Then H is a spanning tree.[2]
  • According to the characteristics of the spanning tree, the spanning tree contains only ∣N ∣ ‐ 1 edges.[3]
  • To set the spanning tree parameters access 'Spanning Tree' under the 'L2 features' tab.[4]
  • For the graph below, use both algorithms to find a minimum cost spanning tree.[5]
  • A port’s role determines how it participates in the spanning tree.[6]
  • The edge ports themselves do send BPDUs to the spanning tree.[6]
  • If the port is the root port, a complete rework of the spanning tree occurs—see When an RSTP Root Bridge Fails.[6]
  • Cisco supports a proprietary Per-VLAN Spanning Tree (PVST) protocol, which maintains a separate spanning tree instance per each VLAN.[6]
  • Let’s start with a formal definition of a spanning tree.[7]
  • Also, we should note that a spanning tree covers all the vertices of a given graph so it can’t be disconnected.[7]
  • An MST follows the same definition of a spanning tree.[7]
  • Like a spanning tree, a minimum spanning tree will also contain all the vertices of the graph .[7]
  • The following one is the spanning tree in the above network.[8]
  • Spanning tree protocol is a distributed algorithm to find the spanning tree of given network topology.[8]
  • After removing the route marked red crosses, we get the spanning tree of the network topology.[8]
  • A spanning tree is a loop-free subset of a network topology.[9]
  • Spanning Tree (PVST) extends the original STP to support a spanning tree instance on each VLAN in the network.[9]
  • A network topology defines multiple possible spanning trees.[9]
  • Even the simplest of graphs can contain many spanning trees.[10]
  • If a graph G is itself a tree, the only spanning tree of G is itself.[11]
  • Spanning Tree (MST) of G is an ST of G that has the smallest total weight among the various STs.[12]
  • We have seen in the previous slide that Kruskal's algorithm will produce a tree T that is a Spanning Tree (ST) when it stops.[12]
  • By generating spanning trees in order of increasing cost, new opportunities appear.[13]
  • In this way, it is possible to determine the second smallest or, in general, the k-th smallest spanning tree.[13]
  • A spanning tree s can be represented by a set of n-1 edges.[13]
  • and i is the rank of s i when all spanning trees are ranked in order of increasing cost.[13]
  • A spanning tree of a graph on vertices is a subset of edges that form a tree (Skiena 1990, p. 227).[14]
  • Since “a spanning tree covers all of the vertices”, it cannot be disconnected.[15]
  • However, A minimum spanning tree is a spanning tree which has minimal total weight.[16]
  • The cost of the spanning tree is the sum of the weights of all the edges in the tree.[17]
  • Minimum spanning tree is the spanning tree where the cost is minimum among all the spanning trees.[17]
  • Algorithm builds the spanning tree by adding edges one by one into a growing spanning tree.[17]
  • In Prim’s Algorithm we grow the spanning tree from a starting position.[17]
  • If we have n = 4 , the maximum number of possible spanning trees is equal to 44-2 = 16 .[18]
  • The root bridge of the spanning tree is the bridge with the smallest (lowest) bridge ID.[19]
  • Both standards implement a separate spanning tree for every VLAN.[19]
  • It creates a spanning tree for each VLAN, just like PVST.[19]
  • In the standard a spanning tree that maps one or more VLANs is called multiple spanning tree (MST).[19]
  • Given a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.[20]
  • A single graph can have many different spanning trees.[20]
  • Check if it forms a cycle with the spanning tree formed so far.[20]
  • WriteLine( "Minimum Cost Spanning Tree" + minimumCost); Console.[20]
  • Minimum diameter spanning tree corresponds to cover by two circles, (b) Point set with high diameter minimum spanning tree.[21]
  • A Spanning tree is a subset of an undirected Graph that has connected all the vertices by minimum number of edges.[22]
  • If all the vertices are connected in a graph, then there will be at least one spanning tree present in the graph.[22]
  • As we studied, one graph may have more than one spanning tree.[22]
  • If there are ’n’ number of vertices, the spanning tree should have n — 1 number of edges.[22]
  • A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges.[23]
  • By this definition, we can draw a conclusion that every connected and undirected Graph G has at least one spanning tree.[23]
  • We found three spanning trees off one complete graph.[23]
  • We now understand that one graph can have more than one spanning tree.[23]
  • Adding just one edge to a spanning tree will create a cycle; such a cycle is called a fundamental cycle.[24]
  • By deleting just one edge of the spanning tree, the vertices are partitioned into two disjoint sets.[24]
  • In graphs that are not connected, there can be no spanning tree, and one must consider spanning forests instead.[24]
  • A single spanning tree of a graph can be found in linear time by either depth-first search or breadth-first search.[24]

소스

  1. ↑ Minimum spanning trees
  2. ↑ 2.0 2.1 Spanning Trees in Graph Theory
  3. ↑ A spanning tree construction algorithm for industrial wireless sensor networks based on quantum artificial bee colony
  4. ↑ Spanish translation – Linguee
  5. ↑ 5.6 Optimal Spanning Trees
  6. ↑ 6.0 6.1 6.2 6.3 Spanning-Tree Protocol Overview
  7. ↑ 7.0 7.1 7.2 7.3 How to Find Total Number of Minimum Spanning Trees in a Graph?
  8. ↑ 8.0 8.1 8.2 Demystifying Spanning Tree Protocol
  9. ↑ 9.0 9.1 9.2 Section 26.2: Spanning Tree Overview
  10. ↑ Minimum Spanning Tree: Definition, Examples, Prim’s Algorithm
  11. ↑ Brilliant Math & Science Wiki
  12. ↑ 12.0 12.1 Minimum Spanning Tree (Prim's, Kruskal's)
  13. ↑ 13.0 13.1 13.2 13.3 An algorithm to generate all spanning trees of a graph in order of increasing cost
  14. ↑ Spanning Tree -- from Wolfram MathWorld
  15. ↑ What is a spanning tree?
  16. ↑ Spanning Tree
  17. ↑ 17.0 17.1 17.2 17.3 Minimum Spanning Tree Tutorials & Notes
  18. ↑ Spanning Tree and Minimum Spanning Tree
  19. ↑ 19.0 19.1 19.2 19.3 Spanning Tree Protocol
  20. ↑ 20.0 20.1 20.2 20.3 Kruskal’s Minimum Spanning Tree Algorithm
  21. ↑ Spanning Tree - an overview
  22. ↑ 22.0 22.1 22.2 22.3 Minimum Spanning Tree Algorithm
  23. ↑ 23.0 23.1 23.2 23.3 Data Structure & Algorithms
  24. ↑ 24.0 24.1 24.2 24.3 Spanning tree

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