cad of vlsi systems intro cntd 4.pdf

7/27/2019 CAD of VLSI Systems intro cntd 4.pdf

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CAD of VLSI Systems

ntro uct on ont ..

Virendra Sin hIndian Institute of Science

Ban [email protected]

E0-285: CAD of VLSI Systems


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CAD of VLSI Systems

z Design of VLSI Systemsz Com lex s stem

z Need systematic methodology

z Can be automated

z ou an e very arge es gns

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Design Domains (Y - Chart)

e ava ora oma n ruc ura oma n

System

Al orithms Processors

Reg. Transfers

Logic

ALU, RAM, ..

Gates, FFs, ..

Transistor Layout

Cell Layout

Module Layout

Floorplan

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Physical Domain

a s ,


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Algorithms

z ost y ntracta e pro ems

z Exact Algorithms

z Branch and Bound

z Dynamic Programmingz Greedy Algorithms

z Soft computing techniques

Ant colony optimization Tabu search etc..

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Algorithms

z

A Graph G(V, E) is a pair (V, E), where V is a setand E is a relation on V

-

vertices

z Undirected Graph edges are unordered pairs

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rc ec ura yn es s

Computation: Differential Equation Solver

xl = x + dx

ul = u 3*x*u*dx 3* *dx

c = xl < a

Data Flow Graph (DFG): represent operation and data

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a a ow rap

1 2

x

3

udx

3 y

u dx x dx

* * +6 8 10

dx ya

xl

* +


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Graph Representation

1 2a

1 2 3 4

1 0 1 1 1

4 3

bed 2 0 0 1 0

3 0 0 0 1

4 0 0 0 0

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Graph Representation

1 2a

2 3 41

4 3

bed

32

43

4

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Graph Algorithms

Shortest Path Algorithms Longest Path Algorithms

Traveling Salesman Problem

ax ma ques

Graph Colouring

Vertex Covering

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n mum pann ng ree


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Graph Algorithms

z

Mostly intractable problemsz Approximate algorithms

z ranc an oun

z

Dynamic Programming

z Soft computing techniques Genetic Al orithms Ant colony optimization Tabu search etc..

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Graph Algorithms

z Shortest Path algorithmsz Di kstras al orithm

110 100

Greedy algorithm

Make local decision reedil

52

Gives shortest path from asource node 3 420

60

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Dijkstras Algorithms

1Iter. S V-S w D[2] D[3] D[4] D[5]

52

30

, , , -

1 {1,2} {3,4,5} 2 10 60 30 100

5010

60 2 {1,2,4} {3,5} 4 10 50 30 90

20 3 {1,2,4,3} {5} 3 10 50 30 60

4 {1,2,4,3,5} 5 10 50 30 60

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Dijkstras Algorithms

z Begin

z S = {1}52

10 10030

z or = o n o

D[i] = C [1,i] initializez = - 3 4

10 60

Choose a vertex w in V-S s.t. D[w] is minimum Add w to S

or eac ver ex v n - o D[v] = Min{D[v], D[w]+C[w,v]}

z end

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Floyds Algorithms

zAll Pair Shortest Path algorithmsz Flo ds al orithm

Make local decision and refine it later

Gives shortest ath for all airs

1 2 32

3

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Floyds Algorithms

1 2 322

3

5

1 2 3

1 0 8 5

1

2

0 8 5

3 0 8

3 2 0 3 2 0

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A0[i,j] A 1[i,j]


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Floyds Algorithms

1 2 322

3

5

1 2 3

1 0 8 5 1

2

0 7 5

3 0 8

3 5 2 0 3 5 2 0

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A2[i,j] A 3[i,j]


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Floyds Algorithmsz Be in

z S = {1}z For I = 2 to n do 1 2 3

2

2

3

A[I,j] = C [i,j] initializez

For I = 1 to n do

5

,

z For k = 1 to n-1 do begin

For i = 1 to n do

For j = 1 to n do If A[I,k]+A[k,j] < A[I,j] then A[I,j] = A[I,k]+A[k,j] =

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,

z end


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Spanning Tree

z ree ree a connec s a e ver ces

z Cost of a spanning tree is sum of edges

z Minimum Spanning Tree (MST)

z Prims AlgorithmGreedy algoritthm

Start from an intial node U = {1}

rows , one e ge a a meAt each step, it finds a shortest edge (u,v) that

connects U and V-U and adds v to V-U from U

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Prims Algorithm

1 1

423

15 5 42

3

15

5 6

3

6

2 2

5 6

3

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Kruskals Algorithm

z Start with a graph t = (V,) only verticesz

z As algorithm progresses,

Have collection of connected componentsz To build progressively larger connected

component

Examine edges for E in order of increasing cost If the edge connects two vertices in two differentconnected component, tthen add edge to T

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Vertex Covering Problem

z Vertex Covering of an undirected graph G

is a subset of the vertices s.t. each edge in

as a eas one e ge n a su se

z Heuristic Select vertex with largest degree Deletion of a vertex corresponds to the removal

of vertex itself and all edges incident to it

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Vertex Covering Problem

1 2 3 4 5

1 2 3 4 5

1 2 1 2

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Graph Colouring Problem

z rap co our ng pro em o an un rec egraph G is a labeling of vertices such that

-same label

number of colours

scan of vertex set where vertices arecoloured one at a time

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cad of vlsi systems intro cntd 4.pdf

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