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Minimum spanning tree

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 that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More…

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Overview

Properties

Algorithms

MST on complete graphs with random weights

Fractional variant

Other variants

Applications

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Map overview Semantic statistics

Minimum spanning tree

Nodes102
Edges101
Triples139
Avg. degree1.98
Density0.019608
Components1

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Minimum spanning tree

Top relations

related to Further reading · 40
Minimum spanning tree → Algorithms, All These Years, Annual Editions, April, Chapter, Charles, Clifford Stein, Cormen, Eisner, Ethnic Relations, Eva Milková, Helena Nesetrilová, Introduction, ISBN, Jaroslav Nešetřil, Jason, John David, Kromkowski, Kruskal's, Leiserson
related to Other variants · 23
Minimum spanning tree → An, Chu, De Morgan's, Esau-Williams, Euclidean, Finding, It, Kruskal's, Liu/Edmonds, Maximum, MBST, MST, Note, NP-complete, NP-hard, Prim's, Sharma, Solving CMST, Steiner, Such
related to Classic algorithms · 22
Minimum spanning tree → Basically, Boruvka, Boruvka's, Borůvka's, By, Cut, Czech, Dijkstra, Each Boruvka, G1, Here, In, Initially, Its, Moravia, MST, Otakar Borůvka, Prim, Prim's, Since
related to Optimal algorithm · 13
Minimum spanning tree → Apply, Contract, Decision, Find, Let, MST, MSTs, Partition, Seth Pettie, The, This, Use, Vijaya Ramachandran
related to MST on complete graphs with random weights · 8
Minimum spanning tree → Alan, Apéry's, For, Frieze, MST, Riemann, Steele, Svante Janson
related to External links · 6
Minimum spanning tree → BGL, Boost Graph LibraryThe Stony, Brook Algorithm Repository, Implemented, Net, QuickGraph
has application · 4
Minimum spanning tree → Christofides, Minimum, Other, They
related to Parallel and distributed algorithms · 4
Minimum spanning tree → If, Research, The, With
is a · 3
Minimum spanning tree → MST in which each vertex is connected to no more than d other vertices, spanning tree of a graph with edge weights corresponding to the Euclidean distance between vertices which are points in the plane, tree that has a marked node
related to Uniqueness · 3
Minimum spanning tree → If, Proof, This

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Important terminology

spanning tree minimum edge graph mst algorithm weight trees edges time weights problem vertices possible optimal number algorithms graphs one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Minimum spanning treeis aspanning tree of a graph with edge weights corresponding to the Euclidean distance between vertices which are points in the plane0.90text
Minimum spanning treeis atree that has a marked node0.90text
Minimum spanning treeis aMST in which each vertex is connected to no more than d other vertices0.90text
the triangle inequalityinstance ofthere is no requirement for edge lengths to obey normal rules of geometry0.80text
determining whether a particular edge is in the MST or determining if the minimum total weight exceeds a certain value are in P.Faster algorithmsSeveral researchers have tried to find more computationally-efficient algorithms.In a comparison modelinstance ofand related decision problems0.80text
in which the only allowed operations on edge weights are pairwise comparisonsinstance ofand related decision problems0.80text
Kargerinstance ofand related decision problems0.80text
Kleininstance ofand related decision problems0.80text
determining whether a particular edge is in the MST or determining if the minimum total weight exceeds a certain value are in Pinstance ofand related decision problems0.80text
Esau-Williamsinstance ofbut good heuristics0.80text
Sharma produce solutions close to optimal in polynomial time.The degree-constrained minimum spanning tree is a MST in which each vertex is connected to no more than d other verticesinstance ofbut good heuristics0.80text
for some given number dinstance ofbut good heuristics0.80text

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