Routing
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ROUTING
The Routing Problem • Apply after placement • Input: – Netlist – Timing budget for, typically, critical nets – Locations of blocks and locations of pins
• Output: – Geometric layouts of all nets
• Objective: – Minimize the total wire length, the number of vias, or just completing all connections without increasing the chip area. – Each net meets its timing budget.
Kinds of Routing • Global Routing
• Detailed Routing
General Routing Paradigm Two phases:
Approaches for Routing • Sequential Approach: – Route nets one at a time. – Order depends on factors like criticality, estimated wire length, and number of terminals. – When further routing of nets is not possible because some nets are blocked by nets routed earlier, apply ‘Rip-up and Reroute’ technique (or ‘Shove-aside’ technique).
• Concurrent Approach: – Consider all nets simultaneously, i.e., no ordering.
Maze Routing Problem • Given: – A planar rectangular grid graph. – Two points S and T on the graph. – Obstacles modeled as blocked vertices.
• Objective: – Find the shortest path connecting S and T.
• This technique can be used in global or detailed routing (switchbox) problems.
Maze Routing S
T
Basic Idea • A Breadth-First Search (BFS) of the grid graph. • Always find the shortest path possible. • Consists of two phases: – Wave Propagation – Retrace
An Illustration S
0
1
2
1
2
3
3
4
5
4
5
3 5 T
6
Wave Propagation
S
• At step k, all vertices at Manhattandistance k from S are labeled with k. • A Propagation List (FIFO) is used to keep track of the vertices to be considered next. S
0
0
1
2
1
2
3
3
S
0
1
2
1
2
3
3
4
3 T
T
After Step 0
After Step 3
5
4
5
3 5 T
After Step 6
6
Retrace • Trace back the actual route. • Starting from T. • At vertex with k, go to any vertex with label k-1. S
0
1
2
1
2
3
3
4
5
4
5
3 5
T
6
Final labeling
Channel Routing
Channel Routing Terminals
Via
Upper boundary Tracks
Dogleg
Lower boundary Trunks
Branches
Channel Routing 0 1 4 5 1 6 7 0 4 9 10 10
2 3 5 3 5 2 6 8 9 8 7 9
How to connect all the points with the same label with the smallest no. of tracks?
Left-Edge Algorithm 1. Sort the horizontal segments of the nets in increasing order of their left end points. 2. Place them one by one greedily on the bottommost available track.
Left-Edge Algorithm 0 1 6 1 2 3 5 6 3 5 4 0 2 4
1. Sort by left end points. 0 1 6 1 2 3 5 6
1 3
5
4
2 6 3 5 4 0 2 4
2. Place nets greedily. 0 1 6 1 2 3 5
6
3 1
5 2
4 6 3 5 4 0 2 4
The Routing Problem • Apply after placement • Input: – Netlist – Timing budget for, typically, critical nets – Locations of blocks and locations of pins
• Output: – Geometric layouts of all nets
• Objective: – Minimize the total wire length, the number of vias, or just completing all connections without increasing the chip area. – Each net meets its timing budget.
Kinds of Routing • Global Routing
• Detailed Routing
General Routing Paradigm Two phases:
Approaches for Routing • Sequential Approach: – Route nets one at a time. – Order depends on factors like criticality, estimated wire length, and number of terminals. – When further routing of nets is not possible because some nets are blocked by nets routed earlier, apply ‘Rip-up and Reroute’ technique (or ‘Shove-aside’ technique).
• Concurrent Approach: – Consider all nets simultaneously, i.e., no ordering.
Maze Routing Problem • Given: – A planar rectangular grid graph. – Two points S and T on the graph. – Obstacles modeled as blocked vertices.
• Objective: – Find the shortest path connecting S and T.
• This technique can be used in global or detailed routing (switchbox) problems.
Maze Routing S
T
Basic Idea • A Breadth-First Search (BFS) of the grid graph. • Always find the shortest path possible. • Consists of two phases: – Wave Propagation – Retrace
An Illustration S
0
1
2
1
2
3
3
4
5
4
5
3 5 T
6
Wave Propagation
S
• At step k, all vertices at Manhattandistance k from S are labeled with k. • A Propagation List (FIFO) is used to keep track of the vertices to be considered next. S
0
0
1
2
1
2
3
3
S
0
1
2
1
2
3
3
4
3 T
T
After Step 0
After Step 3
5
4
5
3 5 T
After Step 6
6
Retrace • Trace back the actual route. • Starting from T. • At vertex with k, go to any vertex with label k-1. S
0
1
2
1
2
3
3
4
5
4
5
3 5
T
6
Final labeling
Channel Routing
Channel Routing Terminals
Via
Upper boundary Tracks
Dogleg
Lower boundary Trunks
Branches
Channel Routing 0 1 4 5 1 6 7 0 4 9 10 10
2 3 5 3 5 2 6 8 9 8 7 9
How to connect all the points with the same label with the smallest no. of tracks?
Left-Edge Algorithm 1. Sort the horizontal segments of the nets in increasing order of their left end points. 2. Place them one by one greedily on the bottommost available track.
Left-Edge Algorithm 0 1 6 1 2 3 5 6 3 5 4 0 2 4
1. Sort by left end points. 0 1 6 1 2 3 5 6
1 3
5
4
2 6 3 5 4 0 2 4
2. Place nets greedily. 0 1 6 1 2 3 5
6
3 1
5 2
4 6 3 5 4 0 2 4
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