Practical Problems in VLSI Physical Design L-RST Algorithm (1/16)

L-Shaped RST Routing Perform L-RST using node b as the root

First step: build a separable MST Prim with w(i,j) = (D(i,j), −|y(i) − y(j)|, − max{x(i), x(j)})

Practical Problems in VLSI Physical Design L-RST Algorithm (2/16)

First Iteration

Practical Problems in VLSI Physical Design L-RST Algorithm (3/16)

Separable MST Construction

Practical Problems in VLSI Physical Design L-RST Algorithm (4/16)

Separable MST Construction (cont)

Practical Problems in VLSI Physical Design L-RST Algorithm (5/16)

Constructing a Rooted Tree Node b is the root node

Based on the separable MST (initial wirelength = 32) Bottom-up traversal is performed on this tree during L-RST

routing

Practical Problems in VLSI Physical Design L-RST Algorithm (6/16)

Partial L-RST for Node C

Practical Problems in VLSI Physical Design L-RST Algorithm (7/16)

Partial L-RST for Node E

Practical Problems in VLSI Physical Design L-RST Algorithm (8/16)

Partial L-RST for Node G

Practical Problems in VLSI Physical Design L-RST Algorithm (9/16)

Partial L-RST for Node D

Practical Problems in VLSI Physical Design L-RST Algorithm (10/16)

Partial L-RST for Node D (cont)

Practical Problems in VLSI Physical Design L-RST Algorithm (11/16)

Partial L-RST for Node F

best case

Practical Problems in VLSI Physical Design L-RST Algorithm (12/16)

Partial L-RST for Node F (cont)

best case

Practical Problems in VLSI Physical Design L-RST Algorithm (13/16)

Processing the Root Node

best case

Practical Problems in VLSI Physical Design L-RST Algorithm (14/16)

Top-down Traversal In order to obtain the final tree

upper upper

lower lower upper

lower lower/upper upper

Practical Problems in VLSI Physical Design L-RST Algorithm (15/16)

Final Tree Wirelength reduction

Initial wirelength − total overlap = 32 − 4 = 28

Practical Problems in VLSI Physical Design L-RST Algorithm (16/16)

Stable Under Rerouting Steiner points are marked X

Wirelength does not reduce after rerouting