Download - Minimal Spanning Tree Problem
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Minimal Spanning Tree Problem
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MST
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MST
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L.Euler 1736 .
. Konigsberg
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. n-1 .
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=40
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45
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G .
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1925 .
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. G .
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44 5
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MST
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:
1956))1957))1965)())
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Joseph Kruskal
Robert C. Prim
Otakar Boruvka
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T T .
T T . n > 0 G
n . T 1
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{0,5} 10
{2,3} 12
{1,6} 14
{2,6} 16
{1,2} 16
{3,6} 18
{4,3} 22
{4,6} 24
{4,5} 25
{0,1} 28
0
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1812
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13() 0
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n-1 . n
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n=10 n=25 n=50 n=75 n=100 n=125
Prim's algorithm 27 41 150 400 960 1800
Boruvka's algorithm 27 35 40 42 60 84
Kruskal's algorithm 27 30 32 34 36 40
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Prim's algorithm Boruvka's algorithm Kruskal's algorithm
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1 e Xe :
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Min z =
S.t. = n-1
(,) S-1 ,
Xe 0,1 e E
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Min z = 2Xab + 3Xac + 4Xbd + 4Xbc + 2Xcd
S.t. Xab + Xbd + Xcd + Xac + Xbc= 3
Xab 1
Xac 1
Xbd 1
Xcd 1
Xbc 1
Xab + Xbc + Xac 2
Xbc + Xcd + Xbd 2
Xe 0,1 e E
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Network flows: theory, algorithms, and applications I Ravindra K. Ahuja Thomas L.
Magnantl James B. Orlin.
On the History of the Minimum Spanning Tree Problem / R.L.Graham Pavol Hell
Comparing minimum spanning tree algorithms / Igor Podsechin
Tampereen lyseon lukio Tietotekniikka
Networks in Action / Gerard Sierksma Diptesh Ghosh
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