CS计算机代考程序代写 algorithm CSE 565 , lecture 12 . 10/06/2021

CSE 565 , lecture 12 . 10/06/2021
Note The pretlow – push algo always maintains a poeftwf
and taking h that are compatible

Fat:_ It flow is a special case of preflow .

Det : We say an edge in .us c- Gf is active , if
hlu) = hw , -11 .

Example

⑤¥¥¥÷÷¥§¥É¥¥±
2

Fanti let t be a pre flow . If there exists an s-t path
in Gf, then there does not exist any labeling h that is

compatible with f- .
Proofs 1 by contradiction )
P in G-f : §→o→→→o→

t .

his)=n hit =o

therefore : its aotpossink to satisfy the steepness condition
for all edges in p , as # ledges in P) = n – i .

Fanti Let f- be a pre flow . It there does not exist an s-t path
in Gf, then there always exist a labeling h that is

compatible with f.
proof : 1 constructive proof,

+

Gf :

S = { u c- V1 s can reach u}
1- = V15

⇒ + c-T . ⇒ IS , IT is an s
-t cat .

Det : hlu) = n , it v c-Shiv) =o , if u E T .
High-level idea of pp algorithm
– maintains f and h that are compatible
– wpdatesfandh 1 path & relabel)
– terminates when f becomesaftow .

Fonti Let f- be a flow . Then the followings are equivalent .
i. there does not exists s – t path in Gt
2. there exists a labeling that is compatible

with f.

3. f is a maximum flow .

Init :

¥¥¥¥÷*5¥. > 0
016)

Gt : ⑤←É-⑤
s¥÷°

fusion
Applies an edge a- lung in Gf .

Xflu)> 0

Applicable:×µu, > o . Ft:
2. e is active

,
e.g.,hiu-hlw-lproadurei-flec-fle-minfxflu.ge#

case / irxfiuyzq ,
saturating -Pash non- saturating push

case 2 : Xfl < Cfl el ¥1 ÷i±¥h .it#+?'" ¥h,it '" ' 4-19 U V 4-19 -Xtlu ✗flu)←Xflu1 -9-14 Xflu)←Xflul - Xfm Xfw)←XfW -19-19 Xfw)←XfWtXf1u) Exampte : Gt : 0¥ old (-147 * 16) push Caa, push " 't! µ⑤←8¥>⑤%)É¥¥%,
a-+ :

*

Fa after push . f- is still apreflow.FI: f- and h are compatible afterpushug .

Rela.be# operation
Applies to a vertex
Applicable to u c- V1 { sit} , if :

1 . Xflu) > 0 .
2. all edges in Ola) are not active
I push can’t be applied)

procedure: hlu) ← him -11 .

Eixample :

Gt :

←É¥⑤”
5 019

1- 147
016)

① relabel (a)

Gt :

¥0s”
5T

c- 14
019

0161

Fatty: hand f- are still compatible -after relabeling .

Algorithm pretlow – push ( G-= 14Th . clekov-ec-E.s.tl .
init h and f.
while ( 7- u c- V1 { sit} sit . Xflu) >0 ) .

arbitrarily pick ns.t.xflu > 0 .

if l I laid C- Etf , Sit . lab is active )| pick arbitrarily such an edge my| push luivelse| yea, man , ,u,
end .

end .

Example :
610) 210)

¥
.

%