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Computer Aided Design: Layout Compaction

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LAYOUT COMPACTION RAJESH YADAV M.TECH VLSI 12ECP01P
COMPACTION The operation of layout area minimization is called layout compaction .
CLASSIFICATION OF COMPACTION ALGORITHMS
PROBLEM FORMULATION • Given: – A set of geometric features M = {M1, M2, ….., Mn}. – The minimum feature size, s(Mi), for all i. – The minimum separation between features Mi and Mj, d(Mi,Mj). • Objective: – Minimize the layout such that size(Mi) ≥ s(Mi) dist(Mi,Mj) ≥ d(Mi,Mj) where size(Mi) and dist(Mi,Mj) are size of Mi and distance between Mi and Mj after the compaction, where 1 ≤ i,j ≤ n.
1-D COMPACTION X followed by Y :
1-D COMPACTION Y followed by X:
2- DIMENSIONAL COMPACTION • 2-D compaction is in general much better than performing 1-D compaction. • 2-D compaction, if solved optimally, produces minimum-area layouts. – It is very time consuming. – Thus 1½-D compaction techniques have been proposed. • Perform x-direction compaction moves while making small moves in the y-direction.
2-D COMPACTION
COMPARISON
1½- DIMENSIONAL COMPACTION • A deterministic algorithm. – Key idea is to provide enough lateral movements to blocks during compaction to resolve interferences. • This is called 1½-dimensional compactor, since the geometry is not as free as in true 2- dimensional compaction.
EXAMPLE • Since C is the lowest block in the ceiling list, it is selected for the move.
CONTD. • The gap is maximum at the boundary between blocks A and B.
CONTD. • The modified layout and the adjacency graph is shown.
CONSTRAINT GRAPH BASED COMPACTION • Constraint graph G = (V,E) – Each vertex v ∈ V represents a component. – The set of edges (E) represents constraints. Constraint Types Connectivity Constraints Separation Constraints
CONNECTIVITY CONSTRAINTS • If two features X and Y are required to be within a distance s of each other. – A physical connection can be represented in the graph as a pair of edges between X and Y, each with weight −s.
SEPARATION CONSTRAINTS • Two features X and Y are required to be at least d units apart from each other. – Represented as an edge from X to Y of weight d.
LONGEST - PATH ALGO FOR DAGs
LIAO – WANG ALGO
APPLICATIONS OF COMPACTION Area minimization Layout compilation Redesign Rescaling
THANK YOU

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Computer Aided Design: Layout Compaction

Editor's Notes

  1. Firstly compaction is done horizontally i.e. in X direction which is followed by vertical compaction i.e. in Y direction. In 1D compaction ->layout elements only move or shrink in one dimension (x or y). Often sequentially performed first in the x-dimension and then in the y-dimension (or vice versa).
  2. An example showing the layout compaction done by moving c block and placing it at a place to get the optimized layout as shown in the next two slides
  3. P-> in degree of the respective node e.g. p1 shows the in degree of the node v1 ,p2 shows in degree of the node v2 and so on. (In degree means the no. of edges entering that node ). X1,x2……x5 shows the longest path from v0 to the node which is being processed . The path 1->5->6->7->3 is the longest path .
  4. Here we consider the longest forward and backward paths and continue until constant path values is found.