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Detailed Routing

Explore detailed routing methodologies for grid-based and gridless models, placement algorithms, and global routing algorithms for optimal circuit design. Learn about channel ordering, terminology, and constraint graphs. Maximize efficiency in routing layers and minimize channel width.

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Detailed Routing

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  1. Detailed Routing مرتضي صاحب الزماني

  2. Projects Schedule • Encounter Tool: 31/3/93 (in person) • Placement Algorithm: 15/4/93 (email) • Global Routing Algorithm: 11/5/93 (in person) مرتضي صاحب الزماني

  3. مرتضي صاحب الزماني

  4. B E E B B B B C D B C D E D B A C A B B C Channel vs Switchbox

  5. B The routing order should be: ??? A D C Channel Ordering A The width of A is not known until A is routed, we must route A first. B BCAD or BCDA مرتضي صاحب الزماني

  6. Channel Ordering No feasible channel order! C D B A 1. Fix the terminals between A & B 2. Route B, C, then D (channel) 3. Route A (switchbox) مرتضي صاحب الزماني

  7. Channel Routing Terminology Terminals Via Upper boundary Tracks Dogleg Lower boundary Trunks Branches مرتضي صاحب الزماني

  8. Grid-Based vs. Gridless Model مرتضي صاحب الزماني

  9. Routing Layer Models 1 Layer VH Model HV Model 2 Layers Layer 1 Layer 2 Layer 3 Via VHV Model HVH Model 3 Layers مرتضي صاحب الزماني

  10. HVH Model Unreserved Layer Model Routing Layer Models VHV Model 1 2 3 3 2 1 Layer 1 Layer 2 Layer 3 Via مرتضي صاحب الزماني

  11. Channel Routing Problem • Input: • Two vectors of the same length to represent the pins on two sides of the channel. • Number of layers and layer model used. • Output: • Connect pins of the same net together. • Minimize the channel width. • (Minimize the number of vias.) • Example: (13002110) • (30120300) • where 0 = no terminal 1 3 0 0 2 1 1 0 3 0 1 2 0 3 0 0 مرتضي صاحب الزماني

  12. Problem Instance and Its Solution مرتضي صاحب الزماني

  13. Constraint Graphs 0 1 6 1 2 3 5 0 1 6 1 2 3 5 1 2 3 4 5 6 6 3 5 4 0 2 4 6 3 5 4 0 2 4 Vertical Constraint Graph: Horizontal Constraint Graph: 6 5 2 1 1 5 4 3 6 3 4 2 Maximum clique = ??? Longest path = ??? مرتضي صاحب الزماني

  14. Vertical Constraint Graphs 0 A C E C E A F H H G 0 B D E B F G 0 D 0 0 Note: Transitive edges are not included B D G E F C H A 21

  15. Lower Bounds on Channel Width 0 1 6 1 2 3 5 6 3 5 4 0 2 4 1. Length of the longest path in the Vertical Constraint Graph (i.t.o. no. of vertices) 2. Channel Density = Maximal clique 0 1 6 1 2 3 5 6 1 2 3 1 4 5 5 6 3 4 6 3 5 4 0 2 4 Local Density 1 3 3 4 4 4 2 2 Lower bound = 4 مرتضي صاحب الزماني Lower bound = 3

  16. Lower Bounds on Channel Width 0 3 1 2 1 2 1 0 2 3 3 Lower bound = 3 مرتضي صاحب الزماني

  17. Cycles in Vertical Constraint Graph • If there is a cycle in the vertical constraint graph, the channel is not routable. • Dogleg can solve the problem. 1 2 1 0 Vertical Constraint Graph 2 0 1 2 2 1 0 2 0 1 مرتضي صاحب الزماني

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