최소 신장 트리

수학노트
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노트

  • An algorithm to construct a Minimum Spanning Tree for a connected weighted graph.[1]
  • The Greedy Choice is to put the smallest weight edge that does not because a cycle in the MST constructed so far.[1]
  • If the graph is not linked, then it finds a Minimum Spanning Tree.[1]
  • For Example: Find the Minimum Spanning Tree of the following graph using Kruskal's algorithm.[1]
  • Find a minimum spanning tree for this graph.[2]
  • One possible minimum spanning tree for this graph are the edges AB,BE,BF,EC,CD.[2]
  • How can we be certain that that edge must be in the final minimum spanning tree?[2]
  • Let’s think about it by contradiction: suppose it wasn’t part of the minimum spanning tree.[2]
  • A minimum spanning tree is a special kind of tree that minimizes the lengths (or “weights”) of the edges of the tree.[3]
  • Initially our MST contains only vertices of given graph with no edges.[3]
  • In other words, initially MST has V connected components with each vertex acting as one connected component.[3]
  • We’ll find the minimum spanning tree of a graph using Prim’s algorithm.[4]
  • This plugin identifies the Minimum Spanning Tree (MST) of geographical inputs.[5]
  • The minimum spanning tree is built gradually by adding edges one at a time.[6]
  • A modification of Kruskal's Algorithm for the solution to the MST problem is presented and is compared with Prim's Algorithm.[7]
  • Minimum spanning trees can be a bit counter-intuitive.[8]
  • Minimum spanning trees are often used to visualize relationships between strains or isolates.[8]
  • The minimum spanning tree of a weighted graph is a set of edges of minimum total weight which form a spanning tree of the graph.[9]
  • The minimum spanning tree can be found in polynomial time.[9]
  • The paper presents a new algorithm based on the distance matrix to solve the LC-MST problem.[10]
  • The studied cases show that the presented algorithm is efficient to solve the LC-MST problem in less time.[10]
  • A minimum spanning tree (MST) can be defined on an undirected weighted graph.[11]
  • An MST follows the same definition of a spanning tree.[11]
  • Like a spanning tree, a minimum spanning tree will also contain all the vertices of the graph .[11]
  • Here, denotes the total number of edges in the minimum spanning tree .[11]
  • A minimum spanning tree, MST(S), of S is a planar straight line graph on S which is connected and has minimum total edge length.[12]
  • Spanning Tree (MST) of G is an ST of G that has the smallest total weight among the various STs.[13]
  • The output is either the actual MST of G (there can be several possible MSTs of G) or usually just the minimum total weight itself (unique).[13]
  • In a weighted graph, a minimum spanning tree is a spanning tree that has minimum weight than all other spanning trees of the same graph.[14]
  • A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem.[15]
  • For simplicity, we assume that there is a unique minimum spanning tree.[15]
  • Then e is part of the minimum spanning tree.[15]
  • Suppose you have a tree T not containing e; then I want to show that T is not the MST.[15]
  • Minimum spanning tree is the spanning tree where the cost is minimum among all the spanning trees.[16]
  • Minimum spanning tree has direct application in the design of networks.[16]
  • There are quite a few use cases for minimum spanning trees.[17]
  • This figure shows there may be more than one minimum spanning tree in a graph.[17]
  • As B is an MST, {e 1 } ∪ {\displaystyle \cup } B must contain a cycle C with e 1 .[17]
  • T is the only MST of the given graph.[17]
  • We have discussed Kruskal’s algorithm for Minimum Spanning Tree.[18]
  • The first set contains the vertices already included in the MST, the other set contains the vertices not yet included.[18]
  • Pick the vertex with minimum key value and not already included in MST (not in mstSET).[18]
  • The Greedy Choice is to pick the smallest weight edge that does not cause a cycle in the MST constructed so far.[19]
  • The spanning-tree condition in our definition implies that the graph must be connected for an MST to exist.[20]
  • If edges can have equal weights, the minimum spanning tree may not be unique.[20]
  • The cut property is the basis for the algorithms that we consider for the MST problem.[20]
  • Prim's algorithm computes the MST of any connected edge-weighted graph.[20]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Kruskal's Minimum Spanning Tree Algorithm
  2. ↑ 2.0 2.1 2.2 2.3 Lecture 32: Minimum Spanning Trees
  3. ↑ 3.0 3.1 3.2 Minimum spanning tree
  4. ↑ Minimum Spanning Tree
  5. ↑ QGIS Python Plugins Repository
  6. ↑ Competitive Programming Algorithms
  7. ↑ Computing minimum spanning trees efficiently
  8. ↑ 8.0 8.1 QIAGEN Bioinformatics Manuals
  9. ↑ 9.0 9.1 Minimum Spanning Tree -- from Wolfram MathWorld
  10. ↑ 10.0 10.1 An efficient method to solve least-cost minimum spanning tree (LC-MST) problem
  11. ↑ 11.0 11.1 11.2 11.3 How to Find Total Number of Minimum Spanning Trees in a Graph?
  12. ↑ Minimum Spanning Trees - an overview
  13. ↑ 13.0 13.1 Minimum Spanning Tree (Prim's, Kruskal's)
  14. ↑ Data Structure & Algorithms
  15. ↑ 15.0 15.1 15.2 15.3 Minimum spanning trees
  16. ↑ 16.0 16.1 Minimum Spanning Tree Tutorials & Notes
  17. ↑ 17.0 17.1 17.2 17.3 Minimum spanning tree
  18. ↑ 18.0 18.1 18.2 Prim’s Minimum Spanning Tree (MST)
  19. ↑ Kruskal’s Minimum Spanning Tree Algorithm
  20. ↑ 20.0 20.1 20.2 20.3 Minimum Spanning Trees

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'minimum'}, {'LOWER': 'spanning'}, {'LEMMA': 'tree'}]
  • [{'LEMMA': 'MST'}]
  • [{'LOWER': 'shortest'}, {'LOWER': 'spanning'}, {'LEMMA': 'tree'}]
  • [{'LEMMA': 'sst'}]
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