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Detailed Routing

Detailed Routing. Projects Schedule. Encounter Tool: 31/3/93 (in person) Placement Algorithm: 15/4/93 (email) Global Routing Algorithm: 11/5/93 (in person). B. E. E. B. B. B. B. C. D. B. C. D. E. D. B. A. C. A. B. B. C. Channel vs Switchbox. B.

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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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