Μέγιστη ροή

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Μέγιστη ροή υνάρτηση χωρητικότητας Κατευθυνόμενο γράφημα 16 13 12 14 7 9 20 4 4 10 αφετηρίακός κόμβος τερματικός κόμβος Ροή δικτύου με τις ακόλουθες ιδιότητες για όλα τα ζεύγη Περιορισμός χωρητικότητας: για όλα τα ζεύγη Αντισυμμετρία: για κάθε Διατήρηση ροής:

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Μέγιστη ροή. Κατευθυνόμενο γράφημα. 12. Συνάρτηση χωρητικότητας. 1 6. 20. 7. 10. 4. 9. αφετηρίακός κόμβος. τερματικός κόμβος. 13. 4. Ροή δικτύου. 14. Συνάρτηση με τις ακόλουθες ιδιότητες. Περιορισμός χωρητικότητας :. για όλα τα ζεύγη. Αντισυμμετρία :. για όλα τα ζεύγη. - PowerPoint PPT Presentation

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

161312147

9204410

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: TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

10/167/1310/127/143/7

913/204/4410

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.. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

10/167/1310/127/143/7

913/204/4410

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.. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

10/167/1310/127/143/7

913/204/4410

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

10/167/1310/127/143/7

913/204/4410

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA ,

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson10/167/1310/127/143/7

913/204/4410 :

1. 0

2.

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA12/167/1312/129/145/7

2/915/204/44101271295

754410465215 Ford-Fulkerson

5/8

3

5

5/8

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11

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2 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA12/167/1312/129/145/7

2/915/204/44101271295

754410465215 Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA12/167/1312/129/145/7

2/915/204/44101271295

754410465215 Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA12/167/1312/129/145/7

2/915/204/44101271295

754410465215 Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA12/167/1312/129/145/7

2/915/204/44101271295

754410465215 Ford-Fulkerson

2

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

12/167/1312/129/145/7

2/915/204/4410

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA .

12/167/1312/129/145/7

2/915/204/4410

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA .

12/167/1312/129/145/7

2/915/204/4410

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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12/1611/1312/1211/147/7

919/204/4410

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9144104231911 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson0/160/130/120/140/7

0/90/200/40/40/10

161312147

9204410 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson0/160/130/120/140/7

0/90/200/40/40/10

161312147

9204410 = 4 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson4/160/134/124/140/7

4/90/204/40/40/10

161312147

9204410 = 4 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson4/160/134/124/140/7

4/90/204/40/40/10

1213847

520441044410 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson4/160/134/124/140/7

4/90/204/40/40/10

1213847

520441044410 = 7 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/160/134/1211/147/7

4/97/204/40/47/10

1213847

520441044410 = 7 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/160/134/1211/147/7

4/97/204/40/47/10

5138117

5741131144313 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/160/134/1211/147/7

4/97/204/40/47/10

5138117

5741131144313 = 8 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/168/1312/1211/147/7

4/915/204/41/40/10

5138117

5741131144313 = 8 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/168/1312/1211/147/7

4/915/204/41/40/10

5512117

5154311114358 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/168/1312/1211/147/7

4/915/204/41/40/10

5512117

5154311114358 = 4 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/1612/1312/1211/147/7

0/919/204/41/40/10

5512117

5154311114358 = 4 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson11/1612/1312/1211/147/7

0/919/204/41/40/10

5112117

1943111193112 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson0/10000/1000

0/10/10000/100010001000

110001000

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson0/10000/1000

0/10/10000/100010001000

110001000

= 1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10000/1000

1/11/10000/100010001000

110001000

= 1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10000/1000

1/11/10000/1000999

1

1000100011999 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10000/1000

1/11/10000/1000999

1

1000100011999 = 1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10001/1000

0/11/10001/1000999

1

1000100011999 = 1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10001/1000

0/11/10001/1000999

1

11999 99999911 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson1/10001/1000

0/11/10001/1000999

1

11999 99999911 = 1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Ford-Fulkerson2/10001/1000

1/12/10001/1000999

1

11999 99999911 = 1... TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp .

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp .

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp .

5512117

5154311114358

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp .

5512117

5154311114358

5112117

1943111193112 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Edmonds-Karp .

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. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic (blocking flow)

33313

2/33/32/31/13/3 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic (blocking flow)

33313

2/33/32/31/13/3 ( )

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic (blocking flow)

34332143

3433243

(0)(1)(1)(2)(2)(3) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic (blocking flow)

34332143

3/31/41/31/32/21/43/3

(0)(1)(1)(2)(2)(3)

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic (blocking flow)

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

34332143

3/31/41/31/32/21/43/3

(0)(1)(1)(2)(2)(3)

34332143

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

33232133

3233

(0)(1)(2)(2)(4)

3/31/41/31/32/211/43/3

111(3)1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

33232133

1/31/231/3

(0)(1)(2)(2)(4)

3/31/41/31/32/211/43/3

111(3)1/1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

32112123

2122

(0)(1)(3)(2)(5)

3/32/42/31/32/21/12/43/3

222(4)22 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3121113

111

(0)(1)(3)(2)

3/33/43/32/31/21/13/43/3

333( )111

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic .

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3433243

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3433243

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

2/34332/242/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

2/34332/242/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3/341/332/21/42/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3/341/332/21/42/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3/341/332/21/42/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3/31/41/31/32/21/43/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

3/31/41/31/32/21/43/3

(0)(1)(1)(2)(2)(3) . .

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Dinic

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

[G. Borradaile and P. Klein, J. ACM56(2), 2009], [J. Erickson, SODA 2010] TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA Hassin Itai-Shiloach st- G, s t . st4537213146357 G . ( .) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAe e , f f, f e e f e. f f.e*ee*ffff

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAc st- G G*.

e* e, , c(e) e.

O(n) [M. Henzinger, P. Klein, S. Rao, and S. Subramanian, JCSS 55(1), 1997]. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

st- G :

(s,t) G.

G*, s* t*, s* (s,t), t* G.

, (s*,t*) G*.

G* s* t*. d(t*) . G d(t*). TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4537213146357 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4537213146357 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4537213146357s*t* TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4537213146357s*t* TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4537213146357s*t* TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA d(j*) s* v* v* G*. (u*, v*) G* (u,v) G, . (u,v)

u v.

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAst4/43/52/30/71/13/31/13/46/63/32/25/7s*t*(2)(4)(7)(9)(3)(4)(6)2/2 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA d(j*) s* v* v* G*. (u*, v*) G* (u,v) G, . (u,v)

u v.

(u*,v*) s* v* (u,v)

(u*,v*) :

. . ( .) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA d(j*) s* v* v* G*. (u*, v*) G* (u,v) G, . (u,v)

u v.

2/30/71/11/1(2)(4)(3)(4) v . v v

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