Download presentation

Presentation is loading. Please wait.

Published byKody Major Modified over 2 years ago

1
© KLMH Lienig Paper: A Unified Theory of Timing Budget Management Presented by: Hangcheng Lou Original Authors: Soheil Ghiasi, Elaheh Bozorgzadeh, Siddharth Choudhuri, Majid Sarrafzadeh 1

2
© KLMH Lienig EECS 527 Paper Presentation Outlines Introduction Problem formulation Solution and algorithm Equivalent formulations Optimal algorithm Extension to other budget policies Weighted budget distribution Bounded budget distribution Min-Max budget distribution Experimental results Q & A 2

3
© KLMH Lienig Timing budgeting versus Path-based placement Delay and placement dilemma Efficiency and performance Previous solutions Zero slack algorithm 3 Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

4
© KLMH Lienig Zero-Slack Algorithm Example 4 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] 2 4 3 6 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [0] [0] [0] [0] [0] [0] [0] [0] O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

5
© KLMH Lienig Zero-Slack Algorithm Example 5 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [0] [0] [0] [0] [0] [0] [0] [0] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

6
© KLMH Lienig Zero-Slack Algorithm Example 6 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1][1] [0] <4,0,4><4,0,4> [1][1] <9,0,9><9,0,9> [1][1] [0] [0] [0] [1][1] [0] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

7
© KLMH Lienig Zero-Slack Algorithm Example 7 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1] [2][2] [1] [1] [0] [0] [0] [1] [0] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

8
© KLMH Lienig Zero-Slack Algorithm Example 8 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1] [2] [1] [1] [2][2] [0] [2][2] [1] [0] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

9
© KLMH Lienig Zero-Slack Algorithm Example 9 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1] [2] [1] [1] [3][3] [0] <7,0,7><7,0,7> [3][3] [1] [0] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

10
© KLMH Lienig Zero-Slack Algorithm Example 10 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1] [2] [1] [1] [3] [1][1] [3] [1] [4][4] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

11
© KLMH Lienig Zero-Slack Algorithm Example 11 Example: Use the zero-slack algorithm to distribute slack Format:, [timing budget] Find the path with the minimum slack Distribute the slacks and update the timing budgets 3 0 I1I1 I2I2 I3I3 I4I4 O1O1 O2O2 [1] [2] [1] [1] [3] [1] [3] [1] [4][4] 2 4 6 O 1 : O 2 : Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

12
© KLMH Lienig DAG G(V,E) model the delay for nodes Goal: Maximize where b denotes the budget on edge e ij. 12 Problem Formulation Formulation by linear programming model (1) (2) (3) d ij is the delay and b ij is the budget T is the timing constraint, largest delay Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

13
© KLMH Lienig Linear Programming Example 13 Problem Formulation Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

14
© KLMH Lienig 14 Problem Formulation Formulation by linear programming model (1) (2) (3) d ij is the delay and b ij is the budget T is the timing constraint, largest delay r ij is defined to be the required timing constraint Define flow supply: Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

15
© KLMH Lienig Basic idea: Maximize the budgets, transform the problem 15 Solution and Algorithm Dual Problem Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

16
© KLMH Lienig Duality 16 Solution and Algorithm Dual Problem Primal (Maximize)Dual (Minimize) i th constraint ≤i th variable ≥ 0 i th constraint ≥i th variable ≤ 0 i th constraint =i th variable unrestricted j th variable ≥ 0j th constraint ≥ j th variable ≤ 0 j th constraint ≤ j th variable unrestrictedj th constraint = Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

17
© KLMH Lienig Duality example Constaint Variable Variable Constraint 17 Solution and Algorithm Primal: Max z = 2x 1 +x 2, x 1 +x 2 ≤ 4, x 1 -x 2 ≤ 2, x 1 ≥ 0, x 2 ≥ 0. Dual: Min v = 4y 1 +2y 2, y 1 +y 2 ≥ 2, y 1 -y 2 ≥ 1, x 1 ≥ 0, x 2 ≥ 0. Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results Primal (Maximize)Dual (Minimize) i th constraint ≤i th variable ≥ 0 i th constraint ≥i th variable ≤ 0 i th constraint =i th variable unrestricted j th variable ≥ 0j th constraint ≥ j th variable ≤ 0 j th constraint ≤ j th variable unrestrictedj th constraint =

18
© KLMH Lienig Min-cost flow problem 18 Solution and Algorithm Source:http://www.math.kth.se/~sasane/SF1811/L6/L6ENG.pdfhttp://www.math.kth.se/~sasane/SF1811/L6/L6ENG.pdf Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

19
© KLMH Lienig 19 Solution and Algorithm Source:http://www.math.kth.se/~sasane/SF1811/L6/L6ENG.pdfhttp://www.math.kth.se/~sasane/SF1811/L6/L6ENG.pdf Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results Min-cost flow problem

20
© KLMH Lienig Example 20 Solution and Algorithm Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

21
© KLMH Lienig Algorithm summary 21 Solution and Algorithm Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

22
© KLMH Lienig Weighted budget distribution Introduce the weight for different net 22 Extension to other budget policies Solution: define new to transform again Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

23
© KLMH Lienig Bounded budget distribution Upper bound is applied to the delay of edge 23 Extension to other budget policies Solution: define backward flow Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

24
© KLMH Lienig Bounded budget distribution Example: nodes a and e --- upper bound =3 Rest of nodes –- upper bound = 4 24 Extension to other budget policies Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

25
© KLMH Lienig Min-Max budget distribution Goal: minimizing the maximum budget minimize the budget skew Solution: binary search on the budget upper bounds 25 Extension to other budget policies Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

26
© KLMH Lienig Experimental Results Environment Xilinx synthesis Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

27
© KLMH Lienig Experimental Results Result 27 Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

28
© KLMH Lienig Experimental Results Result Area and runtime Improve Slice 25.8% on average Improve LUT counts 28.7% on average 28 Introduction Problem Formulation Solution and Algorithm Extension to other budget policies Experimental Results

29
© KLMH Lienig Q&A 29

Similar presentations

OK

ECE 665 - LP Duality 1 ECE 665 Spring 2005 ECE 665 Spring 2005 Computer Algorithms with Applications to VLSI CAD Linear Programming Duality.

ECE 665 - LP Duality 1 ECE 665 Spring 2005 ECE 665 Spring 2005 Computer Algorithms with Applications to VLSI CAD Linear Programming Duality.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on pin diode radiation Ppt on traffic light controller using fpgas Ppt on acid-base indicators experiment Ppt on seasons of the year Ppt on water scarcity in africa Ppt on arithmetic micro operations Ppt on business etiquettes training day cast Ppt on coda file system Ppt on zener diode polarity Free ppt on indian culture