The document discusses layout compaction, which is the operation of minimizing layout area. It classifies compaction algorithms as 1-D, 2-D, or 11⁄2-D. 1-D compaction moves blocks along one dimension only. 2-D compaction produces minimum area layouts but is computationally expensive. 11⁄2-D techniques allow some movement in both dimensions for efficiency. Constraint graph based compaction represents design rules as a weighted graph that can be solved using longest path algorithms. Compaction has applications in area minimization, layout compilation, redesign, and rescaling.

1. LAYOUT
COMPACTION
RAJESH YADAV
M.TECH VLSI
12ECP01P

2. COMPACTION
The operation of layout area minimization is
called layout compaction .

3. CLASSIFICATION OF
COMPACTION ALGORITHMS

4. 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.

5. 1-D COMPACTION
X followed by Y :

6. 1-D COMPACTION
Y followed by X:

7. 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.

8. 2-D COMPACTION

9. COMPARISON

10. 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.

11. EXAMPLE
• Since C is the lowest block in the ceiling list,
it is
selected for the move.

12. CONTD.
• The gap is maximum at the boundary
between blocks A and B.

13. CONTD.
• The modified layout and the adjacency graph
is shown.

14. 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

15. 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.

16. 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.

17. LONGEST - PATH ALGO FOR
DAGs

18. LIAO – WANG ALGO

19. APPLICATIONS OF
COMPACTION
Area minimization
Layout compilation
Redesign
Rescaling

20. THANK YOU