ARCHER:A HISTORY-DRIVEN GLOBAL ROUTING ALGORITHM Muhammet Mustafa Ozdal, Martin D. F. Wong ICCAD ’ 07

Outline Introduction Introduction Problem Formulation Problem Formulation Algorithm Algorithm Experimental Result Experimental Result Conclusion Conclusion

Introduction Circuit densities have been increasing significant. Circuit densities have been increasing significant. DFM rules impose complex constraints on routing problem. DFM rules impose complex constraints on routing problem. Routing problem is typically solved in two steps: global routing and detailed routing. The quality of the final interconnects depends large on the quality of global routing. Routing problem is typically solved in two steps: global routing and detailed routing. The quality of the final interconnects depends large on the quality of global routing.

Introduction The global routing algorithm can be roughly categorized into concurrent and sequential algorithm. The global routing algorithm can be roughly categorized into concurrent and sequential algorithm. Concurrent algorithm is formulated as a combinational optimization problem. The solution close to global optimal but these methods are typically not handle today ’ s large design. Concurrent algorithm is formulated as a combinational optimization problem. The solution close to global optimal but these methods are typically not handle today ’ s large design.

Introduction Sequential algorithm have been proposed to route the nets based on iterative rip-up and reroute ( RNR ) techniques. But it may lead to suboptimal result. Sequential algorithm have been proposed to route the nets based on iterative rip-up and reroute ( RNR ) techniques. But it may lead to suboptimal result. RNR-based global routers are typically greedy in minimize cost function. RNR-based global routers are typically greedy in minimize cost function.

Introduction Non-greedy RNR Non-greedy RNR

Introduction Congestion-driven Steiner tree generation Congestion-driven Steiner tree generation

Problem Formulation Capacity : the number of available track passing through grid edge. Capacity : the number of available track passing through grid edge. Congested : usage (e) > capacity (e) Congested : usage (e) > capacity (e) overflow (e) = usage (e) – capacity (e) overflow (e) = usage (e) – capacity (e)

Algorithm Objective: Objective: 1. Minimize the total congestion history cost of the utilized edge. 1. Minimize the total congestion history cost of the utilized edge. 2. Minimize the total wire length. 2. Minimize the total wire length. 3. Minimize the total usage values of utilized edges. 3. Minimize the total usage values of utilized edges. 1. Initial route based on FLUTE. 1. Initial route based on FLUTE.

Algorithm 2. Each RNR iteration, ripup each congested 2-pin connection and reroute. In the beginning, use I, L, Z pattern route. If a connection failed reroute without congestion in several iteration, it starts to utilize pattern routing with detour or maze routing. 2. Each RNR iteration, ripup each congested 2-pin connection and reroute. In the beginning, use I, L, Z pattern route. If a connection failed reroute without congestion in several iteration, it starts to utilize pattern routing with detour or maze routing. In every K iterations, it improve the Steiner topologies of the nets based on the current congestion level. In every K iterations, it improve the Steiner topologies of the nets based on the current congestion level.

Cost Formulation cost (e) = (1+α*h e k ) * overflow (e) cost (e) = (1+α*h e k ) * overflow (e) h e k : history cost for edge e in iteration k. h e k : history cost for edge e in iteration k. α : history scale factor α : history scale factor

Cost Formulation Based on the value ofα, it categorize iterative algorithm into 3 main phases Based on the value ofα, it categorize iterative algorithm into 3 main phases Initiation Initiation Negotiation Negotiation Convergence Convergence

History-Based Routing of 2-Pin Connections Pattern routing is significantly faster than maze routing. Pattern routing is significantly faster than maze routing. Increasing wirelengths prematurely to avoid congestion can eventually lead to higher overflow. Increasing wirelengths prematurely to avoid congestion can eventually lead to higher overflow.

Congestion Driven Topology Optimization It propose a Lagrangian relaxation based bounded- length minimum-cost topology improvement algorithm. It propose a Lagrangian relaxation based bounded- length minimum-cost topology improvement algorithm. First, create a Hanan grid based on the terminal positions of net. First, create a Hanan grid based on the terminal positions of net.

Congestion Driven Topology Optimization Min-cost Steiner tree is NP-complete. And need to enforce a length bound. Min-cost Steiner tree is NP-complete. And need to enforce a length bound. Lagrangian relaxation : replace each complicated constaint with a penalty term in the objective function. Lagrangian relaxation : replace each complicated constaint with a penalty term in the objective function.

Congestion Driven Topology Optimization

t k : step size used in subgradient method. t k : step size used in subgradient method. As k →∞, t k → 0 and Σt i → ∞. As k →∞, t k → 0 and Σt i → ∞. In this paper, let t k =1/k α, α< 1. In this paper, let t k =1/k α, α< 1. Αprovides a trade-off between quality and convergence speed. Αprovides a trade-off between quality and convergence speed.

Example

Experimental Result

ISPD98 ISPD98

Experimental Result ISPD07 ISPD07

Conclusion Use a method to record some past data and use it to get better solution. Use a method to record some past data and use it to get better solution. Like SA. Like SA. It should slow. It should slow.