Download presentation

Presentation is loading. Please wait.

Published byIsaac Hunt Modified over 3 years ago

1
A Theoretical Study on Wire Length Estimation Algorithms for Placement with Opaque Blocks Tan Yan*, Shuting Li Yasuhiro Takashima, Hiroshi Murata The University of Kitakyushu * Now with University of Illinois at Urbana-Champaign

2
Motivation Opaque blocks makes HPWL inexact Because of IP blocks, analog blocks, memory module… Lead to timing violation, unroutable nets…

3
Motivationcontd Exact wire length estimation for Block Placement the obstacle-avoiding shortest path length Time complexity: O(n)? O(n 2) ? O(nlogn)?... Time complexity is almost the same as HPWL! Already proposed in Computational Geometry However Not well-known in CAD community Need interpretation to be applicable to CAD!

4
Our Contribution We restate the results in [P.J.de Rezende 85] & [M.J.Atallah 91] Simplify the discussion (with Block Placement notions) CAD-oriented language Tailor the theory to fit into Physical Design background

5
Problem Formulation Input: Block location Pin location (on block boundaries) ABLR relations * (obtainable from Sequence Pair, etc) Output: Rectilinear block-avoiding shortest path length for every 2-pin net = Minimal Wire Length (MWL)

6
Assumption 2-pin net s on S, t on T S T S is left-to T y s y t S T s t

7
Locus

8
Theorem 1 MWL = HPWL RU locus of s goes below or through t Proof omitted

9
AB-region

10
Lemma 2 There exists an MWL routing inside the AB-region

11
Horizontal Visibility Graph (HVG)

12
MWL = shortest path length Only linear number of edges, but still captures MWL! Lemma 4: There exists a path (s,t) on the visibility graph that corresponds to an MWL routing.

13
Visibility graph of a placement

14
The overall flow and so on …

15
Time complexity M = # of blocks, N = # of nets Building visibility graph: O(M logM) Estimating one net: O(M) Total: O(M logM + NM) Shortest path on channel graph takes O(NM 2 )

16
Use LUT to enhance the speed No path between two vertices? (a 2 b 2 ) Need to judge whether RU locus above t ? How to find out A & B promptly?

17
Two lemmas: Lemma 5: Two vertices s and t on visibility graph. If there is no path between them, then MWL = HPWL Lemma 6: If t is above ss RU locus and there exists a shortest path between them, then its length = HPWL. MWL(a,b) = HPWL ShortestPath(c,d) = MWL (c,d) = HPWL

18
Theorem 3 The MWL of any two vertices on the visibility graph can be obtained by shortest path algorithm: Shortest path exists, MWL = path length Otherwise, MWL = HPWL

19
How it works MWL = shortest path length No path! MWL = HPWL And so on… Lookup table

20
Time complexity Building LUT: O(M 2 ) Estimating one net: O(1) Total: O(M 2 +N) Almost the same as HPWL!

21
Future works Integration of routing congestion Extension to handle multi-pin nets Application to global router Experimental study

22
Thank you! Q & A

23
Proof of Theorem 1 MWL = HPWL RU locus of s goes below or through t

24
Proof of Lemma 2 There exists an MWL routing completely inside AB-region

25
Proof of Lemma 4 There exists a path p from s to t on HVG that corresponds to an MWL routing.

26
Proof of Lemma 6 If t is above ss RU locus and there exists a shortest path between them, then its length = HPWL.

Similar presentations

OK

Wen-Hao Liu1, Yih-Lang Li, and Cheng-Kok Koh Department of Computer Science, National Chiao-Tung University School of Electrical and Computer Engineering,

Wen-Hao Liu1, Yih-Lang Li, and Cheng-Kok Koh Department of Computer Science, National Chiao-Tung University School of Electrical and Computer Engineering,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power steering Ppt on fire extinguisher types colors Ppt on service marketing 7 p's Ppt on revolution of the earth and seasons quiz Ppt on obesity prevention strategies Ppt on traction rolling stocks Ppt on central limit theorem applet Ppt on stop and wait protocol Ppt on unity in diversity dance Ppt on service oriented architecture diagram