Max flow - Chapter 4 Ø]{»ª* Maximum-flow Problems 1...

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Unformatted text preview: Chapter 4 Ø]{»ª* Maximum-flow Problems 1 •¶ª* 5 8 ˜ÑÕ¦°*•¶ª¸\µ (• ª ¶ µ \ ¸ ª ¶ • * ° ¦ Õ Ñ ˜ µ \ ¸ ª ¶ • * ° ¦ Õ Ñ ˜ ) 6 s 2 3 4 4 8 t 3 8 3 2 6 5 2 2 ð} •¶ª* X8 X•¶ª*8 2 X•¶ª*8 3 Ð 2 »…V P \ bª° ¸ ¦¶ iÑ ˜ •Õ ( residual network) 6 s 2 3 4 4 8 t s 0 6 8 2 3 3 0 0 4 0 8 0 t 0 6 3 8 3 2 6 5 0 0 4 2 05 2 32 4 X a ‰{˜ X ÕbPÑo˜¦ ¸ b • °¶ ª\ bè¶ iª • 0 s 6 8 0 2 3 3 0 0 4 0 8 (a ) ( augmenting path) s t 0 t 0 6 0 4 2 05 32 5 ¨ XV{»ª* 1. ( 2.¦ Õ Ð b° b » b{° W ¦ € Õ ˜Ñ¸ ª ª » { XV 3. s [ (a ) ( augmenting path)? [us , ps ] [∞,-] , ]) xs x V ª X{ » cxy s ) t{ V X»ª b y (ª XV{ »* [ min{ux , 6 cxy}, x {]V X» (a ) ¸R{»ª* 1R. ¸{»ªb 2. Õ¦°b Ð Õ¦°b Ð 3. pn‡ pn 4. Õ¦°b Ð c* pn‡ 2 c* c* c* 7 2 3 2 6 s 8 4 3 2 2 5 6 3 t 4 8 8 2 0 3 2 3 3 0 4 0 4 0 5 8 1 3 0 7 t 8 4 2 0 4 6 0 2 0 3 0 4 2 0 0 2 2 5 6 4 3 0 3 6 s 9 2 3 2 3 s 6 3 2 5 0 4 0 2 4 7 t 10 Ø ÐÕ¦°* xŠµª* 8§6 xŠµª 8§6 8§6¼ [0,6] 14 s 2 (a ) 0 t xŠµª* U U s [0,3] [0,4] [0,2] [0,6] 3 s t 4 [0,8] t [0,3] [0,8] -14 [0,2] 5 11 2 Ñ ˜Õ¦°*Ä鶪¸ 2 ? 1. 8鶪b Î 2. զР* ° ¼ 6 V À à 12 s t Î 8é¶ ª 1 2 0 2 5 s 0 2 0 3 2 0 2 4 1 0 4 3 5 1 0 13 4 0 2 4 5 8 s-2-4-t s-3-5-t s-3-5-4-t s-2-3-4-t s-3-4-t t 3 4 1 2 2 7 3 2 0 5 0 hì Maximize subject to v ∑ xij − ∑ xki = − v j k 0 0 ≤ xij ≤ uij if i = if i = v for all i, j 14 2 Æ È鶪* s1 s s2 2 4 t1 t 3 5 t2 Æ È鶪* Ci i i Ci i’ 15 ...
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Max flow - Chapter 4 Ø]{»ª* Maximum-flow Problems 1...

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