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Mixed Non-Rectangular Block Packing for Non-Manhattan Layout Architectures
M. Wu, H. Chen and J. Jou
Department of EE, NCTU
HsinChu, Taiwan
ISQED 2011
Outline
Introduction Review of B*-trees Problem formulation Floorplanning with isosceles right triangular blocks Floorplanning with the trapezoidal blocks Algorithm Experimental results Conclusions
Introduction
The X architecture is an IC wiring architecture based on the pervasive use of diagonal wires.
Compared with the Manhattan architecture, the X architecture shows a wirelength and reduction of more than 20% and a via reduction of more than 30%.
In order to take full advantage of the X architecture, it is essential to develop new physical design tools for this architecture.
Introduction
Besides rectangular blocks, we can add some blocks which have 45 and 135 degree angle.
By using these flexible blocks, we can obtain more choices for pin assignment and more shapes can be used in floorplans.
Introduction
X-half-perimeter wirelength (XHPWL)
Manhatten bounding box X bounding box
Review of B*-trees The B*-tree is an ordered binary tree for modeling a non-slicin
g floorplan. The root of B*-tree represents the block on the bottom-left cor
ner. If node nj is the left child of node ni, block bj is placed on the ri
ght-hand side and adjacent to block bi. If node nj is the right child of node ni, block bj is placed above
block bi.
Problem Formulation
Input: A set of rectangular blocks B A set of isosceles right triangular blocks T Some blocks from B and T will form a trapezoidal block
Output: A floorplan F for each block in set B and set T such that n
o two blocks overlap and the shapes of trapezoidal blocks can be maintained
Objective: Optimize a predefined cost metric, such as the area or XH
PWL minimization
Floorplanning with Isosceles Right Triangular Blocks
Feasibility condition for mixed isosceles right triangular and rectangular blocks
Compact floorplan for (a) and (b)The deadspaces of (a) and (b) are quite large
The packing with isosceles right triangular blocks
The isosceles right triangular blocks are classified into four kinds according to the position of right angles.
The packing with isosceles right triangular blocks
Case BR:
b
BR HtBR
xb, yb
xtBR, ytBR
BR
b
xb+Wb-xtBR
Wb
WtBR
xb, yb
xtBR, ytBR
The packing with isosceles right triangular blocks
Case BL:
BL
bxb-xtBL
Wb
HtBLBL
b
HtBLHtBL-(xb-xtBL)
The packing with isosceles right triangular blocks
Case TR:
TR
b Hb
TR
b
WtTR
(xtTR+WtTR)-(xb+Wb)Hb
Wb
Hb-[(xtTR+WtTR)-(xb+Wb)]
The packing with isosceles right triangular blocks
Case TL:
b Hb
TL
bxb-xtTL
Hb
TL
Hb-(xb-xtTL)
The packing with isosceles right triangular blocks
Case TR vs BL:
Case TL vs BR:
BLTR
xtbu, ytbu
xtbd, ytbd
TL
BR
Htbd
Wtbu
xtbu+Wtbu-xtbd
xtbu-xtbd
xtbu, ytbu
xtbd, ytbd
Floorplanning with the Trapezoidal Blocks
Feasiblity condition for mixed trapezoidal and rectangular blocks
Horizontal trapezoid blocks Vertical trapezoid blocks
Packing with B*-tree scheme, tL and tR have falling down problems
Floorplanning with the Trapezoidal Blocks
B*-trees and corresponding packing scheme with trapezoidal blocks
Floorplanning with the Trapezoidal Blocks
For falling down problems, we need to calculate the heights of the corresponding dummy blocks:
Floorplanning with the Trapezoidal Blocks
Vertical trapezoidal block
Algorithm
Algorithm
The B*-tree is perturbed to another by the following operations:
Op1: Rotate a block Op2: Flip a block Op3: Move a block to another place Op4: Swap two blocks Op5: Move a trapezoidal block to another place
Experimental Results
Experimental Results
Experimental Results
Conclusions
This paper presented an efficient algorithm to handle the floorplanning with isosceles right triangular blocks based on the B*-tree representation.
The proposed algorithm can deal with all shapes which are the combination of rectangle and isosceles right triangle.
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