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An Introduction to Channel Routing 曾奕倫 元智大學資訊工程系 2008/07/11.

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Presentation on theme: "An Introduction to Channel Routing 曾奕倫 元智大學資訊工程系 2008/07/11."— Presentation transcript:

1 An Introduction to Channel Routing 曾奕倫 元智大學資訊工程系 2008/07/11

2 A Channel Routing Problem 2

3 A Channel Routing Problem (cont’d) 3

4 4

5 A Solution to the Channel Routing Problem 5

6 A Solution to the Channel Routing Problem (in VLSI Physical Design) 6  Different colors represent different layers.

7 A Solution to the Channel Routing Problem (cont’d) Minimizing the number of tracks means minimizing the routing area. 7

8 A Channel Routing Problem 8

9 A Channel Routing Problem (cont’d) 9

10 Description of a Channel Routing Problem 10 # Description of a Channel Routing # Problem Columns: Nets: A B C D E F Top_Row: C NULL F E B NULL A Bottom_Row: A NULL NULL B NULL B C Left_Nets: A D F Right_Nets: D E (The Input to Your Channel Router)

11 Vertical Constraint Graph 11  At column 1, the horizontal segment of net C must be placed above the horizontal segment of net A.

12 Vertical Constraint Graph (cont’d) 12  At column 1, the horizontal segment of net C must be placed above the horizontal segment of net A.

13 Vertical Constraint Graph (cont’d) 13  At column 4, the horizontal segment of net E must be placed above the horizontal segment of net B.

14 Vertical Constraint Graph (cont’d) 14  At column 7, the horizontal segment of net D must be placed above the horizontal segment of net C. VCG

15 The Left-Edge Algorithm Proposed by Hashimoto and Stevens in 1971 Regarded as the first channel routing algorithm Can be used in solving Channel Routing Problems Originally used in PCB design Can be applied on VLSI physical design Requires building the Vertical Constraint Graph (VCG) for a channel routing problem 15

16 The Left-Edge Algorithm (cont’d) Step 1: Build VCG 16

17 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 17  Consider horizontal segments of N1, N4, and N10 (the nets that do not have ancestors)

18 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 18  N1 has the smallest x coordinate  N1 and N4 cannot be placed on the same track  N1 and N10 can be placed on the same track  Place N1 and N10 on the highest track

19 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 19  N1 has the smallest x coordinate  N1 and N4 cannot be placed on the same track  N1 and N10 can be placed on the same track  Place N1 and N10 on the highest track

20 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 20  Update the VCG (remove N1 and N10 from the VCG)

21 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 21  Update the VCG (remove N1 and N10 from the VCG)

22 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 22  Consider horizontal segments of N4 and N7 (the nets that do not have ancestors)

23 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 23  Consider horizontal segments of N4 and N7 (the nets that do not have ancestors)

24 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 24  Consider horizontal segments of N4 and N7 (the nets that do not have ancestors)  N4 has the smallest x coordinate  N4 and N7 cannot be placed on the same track  Place N4 on the second highest track

25 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 25  Consider horizontal segments of N4 and N7 (the nets that do not have ancestors)  N4 has the smallest x coordinate  N4 and N7 cannot be placed on the same track  Place N4 on the second highest track

26 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 26  Update the VCG (remove N4 from the VCG)

27 The Left-Edge Algorithm (cont’d) Step 2: Place horizontal segments 27  Update the VCG (remove N4 from the VCG)  Repeat the placement iterations …

28 The Left-Edge Algorithm (cont’d) - Result of the Example 28

29 The Left-Edge Algorithm (cont’d) - Result of the Example 29 N1 = 5 N2 = 1 N3 = 2 N4 = 4 N5 = 3 N6 = 2 N7 = 3 N8 = 1 N9 = 2 N10 = 5 (The Output of Your Channel Router)

30 The Left-Edge Algorithm (summary) Step 1: Build the Vertical Constraint Graph (VCG) for the input channel routing problem Step 2: Place horizontal segments (choose nets (1) that do not have ancestors in the VCG and (2) whose horizontal segments do not overlap) and update the VCG Step 3: Repeat Step 2 until all the horizontal segments have been placed 30

31 A Channel Routing Problem Dogleg Channel Routing 31

32 A Channel Routing Problem (cont’d) 32 VCG Loop  The Left-Edge Algorithm cannot deal with a channel routing problem whose VCG contains loops.

33 Channel Density 33  Channel Density = 5  At least 5 tracks are required in order to solve this channel routing problem (with or without doglegs).

34 To-Do List Choose a Programming Language Implement a Graphical User Interface (GUI) for displaying (1) a channel routing problem (the input) and (2) its solution (the output) Implement the Left-Edge Algorithm – Build the VCG (step 1) Data Structure (Adjacency List) How to find nets that have no ancestors in the VCG How to delete nets from the VCG – Placement of horizontal segments (step 2) How to check the existence of loops in a VCG 34


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