Multi-Threaded Collision-Aware Global Routing with Bounded-Length Maze Routing

1. Multi-Threaded Collision-Aware Global Routing with Bounded-Length Maze Routing Wen-Hao Liu, Wei-Chun Kao, Yih-Lang Li, and Kai-Yuan Chao DAC 2010

2. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

3. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

4. Introduction • ISPD’07 and ’08 global routing contest encouraging the development of global router. • Maze routing is still the most important part in those routers, and heavily affects runtime and routing quality. • However, those routers seldom attempt to develop new approaches to improve it.

5. Introduction (cont.) • Multi-core architecture becomes the mainstream. • Partitioning-based concurrency is difficult to control load balancing and hence the speedup strategy tends to be limited.

6. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

7. Problem Formulation supply s(e) the number of available routing tracks passing through an edge e demand d(e) the number of wires that utilize an edge e Global bins Global bins Cells Global edges Global edges • Wirelength is as small as possible 7

8. Preliminaries • Time complexity of maze routing. • O(VlogV), V is the size of search region • Many routers use bonding box to limit the search region. • If no overflow-free path exist, expand the bonding box • The limitation may waste routing resources.

9. Motivated example • (a) routing result with bonding box • (b) routing result without bonding box

10. Motivated example (cont.) • We want a approach that is not only restricts the searching region to speed up maze routing, but also effectively utilizes routing resources by avoiding producing redundant wirelength. • Develop BLMR

11. Bounded-Length Maze Routing • Identifying a minimal-cost path from a net’s source to the target with a specified length constraint. • Consider not only length but also cost of each net.

12. The proposed global router • Adopting Bounded-Length Maze Routing (BLMR) • 3D routability-driven • Objective: minimize the followings • Maximum overflow • Total overflow • Total wirelength • Runtime

13. Design flow of the proposed router

14. Design flow of the proposed router (cont.) • Compact 3D routing problem into 2D • Do layer assignment [14] at the end of the flow • Use MST to decomposed each net into two-pin nets • Generates an initial congestion graph via monotonic routing • Negotiation-based rip-up & reroute adopting BLMR

15. Monotonic Pattern Routing Proposed in FastRoute 2.0 [ASPDAC07] Finds the routing path in the direction toward T within the bounding box formed by S and T Can be done by dynamic programming with the same complexity as Z-shaped pattern routing T S 15

16. Layer Assignment p3 p’3 p’2 p’1 p2 p1 p4 Compression One-layer routing p3 p’3 Layer Assignment p2 p’2 p’1 p1 p4

17. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

18. Some notations

19. Optimal-BLMR • Obtains a minimum-cost routing solution under the bounded-length constraint. • Search region V wl(Pi)=Manh(s,v)=5 Manh(v,t)=4

20. Two policies of Optimal-BLMR • Prunes the path with bounded-length violation and restricts the searching region. • Reserve all paths that are not been dominated by others. • If P1(s ,v) has longer wirelength and higher cost than P2(s, v), P1(s, v) is said to be inferior to P2(s, v), and can be discarded.

21. Examples • Two path candidates P1(s, v) and P2(s,v) from s to v: the gray regions are congested regions, the bounded length is 16, and pc(P1), pc(P2), wl(P1) and wl(P2) are 80, 90, 11 and 5, respectively. • P1 has lower cost but not enough length slack. • Thus, BLMR cannot reserve the min-cost path only.

22. But why keeping both of them? • Because the wirelength from v to t is uncertain before the end of routing, optimal-BLMR must reserve both paths. We do not know the routing length

23. Disadvantage of Optimal-BLMR • May not be suited to solve modern large-scale designs. • Hence, heuristic-BLMR approach is proposed.

24. Heuristic-BLMR • Reserves only one path from the source to the current node, and the other paths are discarded. • Cannot guarantee the optimal solution but faster. • How to decide which path should be reserved?

25. Heuristic-BLMR (cont.) • Reserve the minimal-cost path with enough length slack. • If no path candidates have enough length slack, reserve the shortest path candidate for its greater chance to bypass the congested regions. • Need to estimate the wirelength from v to t.

26. History-based estimated wirelength • ewk(v,t) is the history-based estimated wirelength from v to t in iteration k • k represents the iteration number of the global routing • Lk-1(s,t) is the history length, i.e., actual routed wirelength from s to t in iteration k-1

27. History-based estimated wirelength (cont.) • Heuristic-BLMR predicts that Pi(s,v) has sufficient length slack to bypass the congested regions from v to t if the following equation holds

28. Bounded-length relaxation • In the rip-up & reroute (R&R) stage, relaxing the bounded length encourages heuristic-BLMR to obtain routing results with less overflow at the cost of using longer wirelength. • Scheme: • is the bounded length of net n in the k-th routing iteration • .αandβare are user-defined constant

29. Phase1 Phase2 Phase3

30. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

31. Task-Based Concurrency Strategy on Multi – Core Platform • Applied in rip-up & reroute stage to speed-up. • R&R may take 99.6% runtime of the entire routing flow • To keep all threads working with almost full load during routing. • Can explore more concurrency than partitioning-based approach

32. What is Task-Based Concurrency Strategy (TCS)? • Main ideas • A two-pin net routing is defined as a task • A task queue is maintained to contain all tasks • Update queue iteratively • Each thread repeatedly acquires a task from the task queue when the thread completes its task

33. Example of two concurrency strategies • TCS may have race condition between thread

34. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

35. Collision • Due to two or more threads demand the same routing resource simultaneously. • Inconsistency • Often occurs when several nets are close to each other in a congested region, when the nets are routed simultaneously.

37. Collision-Aware R&R • An overflow net often only contains a few overflow grid edges. • The overflow net only needs a few detours to avoid congested regions • The bounded-length of a net is incrementally relaxed • Thread may reuse most grid edges of the original path in the new path

38. Collision-Aware R&R (cont.) • Hence, it is useful to avoid collisions by preventing new routing paths from passing through the original routing paths of other currently routed nets.

40. Outline • Introduction • Preliminaries • Bounded-Length Maze Routing • Task-based Concurrency Strategy • Collision-aware rip-up & reroute • Experimental results and Conclusions

41. Experimental results • Environment • C/C++ • Quad-core 3.0 GHz Intel Xeon-based PC • 32GB memory

42. Routing Results of SequentialGlobal Routers– overflow-free cases • Use proposed SGR adopting BLMR in R&R stage • Only this and FastRoute adopt a single set of control parameters to solve all benchmarks

43. Routing Results of SequentialGlobal Routers– hard-to-route cases • Faster but still keep quality

44. Comparison between proposed SGR and collision-aware PGR – overflow-free cases • Race condition may result in nondeterministic routing result • Collision-aware PGR is performed 10 times

45. Comparison between proposed SGR and collision-aware PGR – hard-to-route cases

46. Conclusions • First addresses the BLMR problem and develop solving algorithms. • Compared to other modern global routers, the proposed global router using heuristic-BLMR identifies less wirelength with less runtime. • Develop PGR adopts TCS and collision-aware R&R to increase CPU utilization and estimate collision