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.