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Minim ln kostra grafuPetr Chalupa a Sven Dra anIV104 Semin program torsk ch Trocha historie Otakar Bor vka 1899 1995 .
V roce 1926 pou il tento algoritmus p i pokusuo sestaven efektivn elektrick rozvodn s t pro Moravu Znovuobjevil Choquet 1938 a po n m je t Florek Lukaziewicz Perkal Stienhaus a.
Zubrzycki 1951 a znovu Sollin po tkem 60 Proto e Sollin z nich byl jedin informatik zez padu b v tento algoritmus obzvl t vliteratu e o paraleln ch v po tech miln ozna ov n jako Sollin v .
Minim ln kostra grafu Petr Chalupa Sven Dra an 2 Trocha historie Bor vk v algoritmus1 Vezm me graf G mno inu vrchol V a pr zdnoumno inu hran .
2 Do ka d komponenty spojitosti zpo tkujednoprvkov p idej hranu a s n souvisej c vrchol takovou aby pr v jeden vrchol byl vkomponent a ohodnocen bylo minim ln 3 Dokud existuje v ce jak jedna komponenta.
spojitosti potom prov d j 2 Jedn se o jakousi paraleln verzi Jarn kovaalgoritmu Minim ln kostra grafu Petr Chalupa Sven Dra an 3 Trocha historie.
Vojt ch Jarn k 1897 1970 Objevil roku 1930 algoritmus dnes zn m jako jako Prim v proto e jej nez visle nan m objevil Robert C Prim roku 1957 a pot znovuobjevil 1959 E W Dijkstra .
1 Do mno iny vrchol V vlo libovoln vrchol grafu amno inu hran E vezmi pr zdnou 2 Do V p idej hranu minim ln d lky takovou aby pr v jeden z jejich vrchol byl ve V 3 Dokud m e opakuj 2 .
4 Minim ln kostra grafu je E Minim ln kostra grafu Petr Chalupa Sven Dra an 4 Trocha historie Joseph B Kruskal 1929 1 M jme mno inu L komponent spojitosti na.
po tku jednoprvkov ch a mno inu v echhran H grafu G 2 Z H vezm me hranu s minim ln mohodnocen m spojuje li r zn komponentyspojitosti dejme ji do mno iny M a slu me.
dan komponenty jinak ji zaho me 3 Dokud nen H pr zdn opakuj 2 4 Minim ln kostra je M Minim ln kostra grafu Petr Chalupa Sven Dra an 5 Slo itosti.
Jarn k v Prim v O E Bor vl v Sollin v O E log V Kruskal v O E log V t d n hran O E log E O E hled n kostry O E V .
kde je inverzn AckermannovaMinim ln kostra grafu Petr Chalupa Sven Dra an 6 Ackermannova funkceA 1 1 1 A 2 2 22 A 3 3 33 3 Roste nade v echny meze a je p kladem.
vysoce rekurzivn funkce proto se pou v p itestech kompil tor jej inverze se v b n chmez ch aproximuje hodnotou 4 Minim ln kostra grafu Petr Chalupa Sven Dra an 7 Implementace.
Vyhled vac algoritmy Petr C Nymfe Testovac data Petr a Sven C Pascal Perl PC Nymfe Vizualizace Sven.
Borland Delphi 7 0 PCMinim ln kostra grafu Petr Chalupa Sven Dra an 8 Testovac data pln grafMinim ln kostra grafu Petr Chalupa Sven Dra an 9 Testovac data pln graf.
Minim ln kostra grafu Petr Chalupa Sven Dra an 10 Testovac data pln grafMinim ln kostra grafu Petr Chalupa Sven Dra an 11 Testovac data pln grafMinim ln kostra grafu Petr Chalupa Sven Dra an 12.
Testovac data pln grafMinim ln kostra grafu Petr Chalupa Sven Dra an 13 Testovac data pln grafMinim ln kostra grafu Petr Chalupa Sven Dra an 14 V sledky pln graf.
Po et Jarn k Kruskalvrchol 160 as pam as pam 500 0 49 4732 1 06 72641000 2 00 10888 4 94 24212.
1500 5 07 51872 12 07 89104 802000 9 11 35484 22 55 89156 6010107 17554 402500 14 44 36 5119937 34840.
3000 21 68 54 84500 1000 1500 2000 2500 3000 3500 400019937 348403500 29 86 77 836 4 Jarn k as Kursak as.
19937 101 4 348424000 38 20Minim ln kostra grafu Petr Chalupa Sven Dra an 15 Testovac data R iceMinim ln kostra grafu Petr Chalupa Sven Dra an 16.
Testovac data R iceMinim ln kostra grafu Petr Chalupa Sven Dra an 17 Testovac data R iceMinim ln kostra grafu Petr Chalupa Sven Dra an 18 Testovac data R ice.
Minim ln kostra grafu Petr Chalupa Sven Dra an 19 Testovac data Pampeli kyMinim ln kostra grafu Petr Chalupa Sven Dra an 20 Testovac data Pampeli kyMinim ln kostra grafu Petr Chalupa Sven Dra an 21.
Testovac data Pampeli kyMinim ln kostra grafu Petr Chalupa Sven Dra an 22 Testovac data Pampeli kyMinim ln kostra grafu Petr Chalupa Sven Dra an 23 V sledky Pampeli ky.
Po et Jarn k Kruskal pam pam 1000 0 10 3208 0 19 3756 45000 1 65 11220 2 92 21608 11000 5000 10000.
10000 3 97 19516 6 34 46304 Jarn k as Kursak asMinim ln kostra grafu Petr Chalupa Sven Dra an 24 Testovac data M kaMinim ln kostra grafu Petr Chalupa Sven Dra an 25 Testovac data M ka.
Minim ln kostra grafu Petr Chalupa Sven Dra an 26 Testovac data M kaMinim ln kostra grafu Petr Chalupa Sven Dra an 27 Testovac data Bludi t Minim ln kostra grafu Petr Chalupa Sven Dra an 28.
V sledky Bludi t Po et Jarn k Kruskalvrchol 0 6 pam pam 1000 0 02 2484 0 01 1540.
5000 0 13 3116 0 10 36881000 5000 1000010000 0 54 3508 0 20 4576 Jarn k as Kursak asMinim ln kostra grafu Petr Chalupa Sven Dra an 29 Testovac data Strom.
Minim ln kostra grafu Petr Chalupa Sven Dra an 30 Testovac data StromMinim ln kostra grafu Petr Chalupa Sven Dra an 31 V sledky StromPo et Jarn k Kruskal.
pam pam 0 31000 0 01 1540 0 01 15405000 0 05 1544 0 04 15441000 5000 10000Jarn k as Kursak as.
10000 0 28 2988 0 11 3556Minim ln kostra grafu Petr Chalupa Sven Dra an 32 Reference http cs wikipedia org http en wikipedia org.
Minim ln kostra grafu Petr Chalupa Sven Dra an 33Minimální kostra grafu – Petr Chalupa, Sven Dražan Vyhledávací algoritmy – Petr C++, Nymfe Testovací data – Petr a Sven C++, Pascal, Perl, PC, Nymfe Vizualizace – Sven Borland Delphi 7.0, PC Minimální kostra grafu – Petr Chalupa, Sven Dražan Minimální kostra grafu – Petr Chalupa, Sven Dražan Minimální kostra grafu ...

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