ece6133 final project implementation of the a-tree algorithm · ece6133 final project the a-tree...

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Implementation of ECE6133 Final Project

Implementation of the A-Tree Algorithm

Thomas Moon

ContentsContents

Problems in A-tree1

Modified A-tree2

Demo3

Result4

1 Problems in A-tree1.Problems in A-tree

1. Do we need to perform H-move?

S1: dx≥df dy≥df dx p

mx

S1: dx≥df, dy≥dfS2: dx≥df, dy<dfS3: dx<df dy≥df

p

dydfmfwS3: dx<df, dy≥df

H : dx<df, dy<dfmfs

mfw my

s


HH H Set of root

nodes in 1-H

H HH

H H

nodes in 1quadrant

H

…

source(0,0)


H-move=> dx<df, dy<df

H(x,y_max)

NW h ld hNW should haveno root node

…dx=∞, df=# => dx>df

S-move


2. Node IsolationROOT={a,b,c}

b

63 dx dy df mfw mfs move

{ , , }

a

a7

a 6 ∞ 7 c c S3

a a’

a

S3: dx<df, dy≥dfa

c9

f(a)=min{ distx(mfw(a,Fk),a), dx(p,Fk) }

a aS3 move: f(a)

4s =min{ distx(c,a), dx(p,Fk) }

=min{ 0, 6 } = 0


2. Node IsolationROOT={a’,b,c}

a

b


{ , , }

S1: dx≥df, dy≥df

a’ a

7

a’ 6 ∞ 0 a a S1

mfwamfw a

c9

mfwS1 move: ’mfw ’

4s


2. Node IsolationROOT={b,c}

a

b


{ , }

a’ a

7

b ∞ 10 16 s s S2

c9

4s

Problems in A-treeProblems in A-tree

2. Node IsolationROOT={b’,c}

3 a

b


{ , }

a’ a

7

b’ ∞ ∞ 6 s s S1

c9

b’

4s


2. Node IsolationROOT={c}

3 a

b


{ }

a’ a

7

c ∞ ∞ 6 b’ b’ S1

c9

b’

4s


2. Node IsolationROOT={.}

3 a

b

6

{ }

a’ a

7

c9

b’

4s

2 Modified A-tree2.Modified A-tree

What’s wrong?ROOT={a,b,c}

b


{ , , }

a

a7

a 6 ∞ 7 c c S3

a a’

a

a

c9

min{ distx(mfw(a,Fk),a), dx(p,Fk) }

a aS3 move:

4s min{ distx(c,a), dx(p,Fk) }

min{ 0, 6 } = 0


Overlapped Steiner-pointROOT={a’,b,c}

b


{ , , }

a

a

a

7

a’ 6 ∞ 0 a a S1a’

aa aa

c9 S1 move: ’a ’

4s


Modify S2 & S3When disty(mfs(a,Fk),a) =0 in S2When disty(mfs(a,Fk),a) 0 in S2=>”H-S2”When dist (mfw(a F ) a) =0 in S3When distx(mfw(a,Fk),a) =0 in S3=>”H-S3”


Simple proof

SH H

H-S

H

H HH

H HH

…source(0,0)

At least one S-move or H-S-move


Modify S2 & S3When disty(mfs(a,Fk),a) =0 in S2When disty(mfs(a,Fk),a) 0 in S2=>”H-S2”=>Choose dy instead of dist>Choose dy instead of distyWhen distx(mfw(a,Fk),a) =0 in S3=>”H S3”=> H-S3=>Choose dx instead of distx


Move PriorityMove Priority

S H-S H


1. No IsolationROOT={a,b,c}

b


{ , , }

a

7

a 6 ∞ 7 c c S3a

c9

f(a)=min{ distx(mfw(a,Fk),a), dx(p,Fk) }

H-S3

4s =min{ distx(c,a), dx(p,Fk) }

=min{ 0, 6 } = 0 => 6

Modified A-treeModified A-tree

1. No IsolationROOT={a,b,c}

b


{ , , }

a

7

a 6 ∞ 7 c c S3aa

’

c9

min{ distx(mfw(a,Fk),a), dx(p,Fk) }

H-S3

4s min{ distx(c,a), dx(p,Fk) }

min{ 0, 6 } = 0 => 6

Modified A-treeModified A-tree

2. Reduce ComputationAccept the first S-move and breakAccept the first S move and break


3. No 1-Quadrant ConstraintSo far, Dual-Quadrant ver.So far, Dual Quadrant ver.Original A-tree on each quadrant

VSVSAlternative…


A-tree on each quadrant

Wire Length = 159


Virtual node on the pole

Wire Length = 151Wire Length 151

3 Demo3.Demo

4 Result4.Result

Run timeBase: compute entire root nodeModified: accept 1st S-moveModified: accept 1 S-move

0.45

0.5

0.3

0.35

0.4

me(s

ec)

0.15

0.2

0.25

Execu

tio

n t

i

base

modified

0

0.05

0.1

100 150 200 250 300100 150 200 250 300

# of Initial nodes

4 Result4.Result

Wire LengthBase: perform A-tree on each quad.Modified: use vertual nodesModified: use vertual nodes

700

750

600

650

700

Len

gth

450

500

550

Wir

e L

base

modified

400

450

100 150 200 250 300

# of Initial nodes

ece6133 final project implementation of the a-tree algorithm · ece6133 final project the a-tree...

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