UNIFICATION OF OBSTACLE-AVOIDING RECTILINEAR STEINER TREE CONSTRUCTION

1. UNIFICATION OF OBSTACLE-AVOIDING RECTILINEAR STEINER TREE CONSTRUCTION Iris Hui-Ru Jiang, Shung-Wei Lin and Yen-Ting Yu Department of Electronics Engineering & Institute of Electronics National Chiao Tung University, Hsinchu 300, Taiwan SOC Conference, 2008 IEEE International

2. ABSTRACT • This paper unifies obstacle-avoiding rectilinear Steiner tree construction either for single(SL-OARSMT) or for multiple(ML-OARSMT) routing layers.

3. INTRODUCTION • define a generic procedure of OARSMT construction

4. Design step • step 1 projects all pins onto a pseudo plane and constructs a DT(Delaunay triangulation) over them. • step 2 grows up an obstacle-weighted MST on the DT with good estimation on obstacle penalties. • step 3, edge by edge, rectilinearizes each tree edge and then reduces cost by novel three-dimensional U-shaped pattern refinement. • Steps 1 and 2 are performed on the pseudo plane, while step 3 is performed in the 3D space.

5. Feature • (1) We unify OARSMT construction into one procedure. • (2) During DT construction, we add extra edges that may lead to more desirable solutions. • (3) Unlike the conventional planar U-shaped pattern refinement, we present a novel three-dimensional method.

6. Compare the techniques

8. PROBLEM FORMULATION • pin-vertex pi is a vertex (xi, yi, zi) on a layer zi • while a via (xj, yj, zj) on layer zj is an edge between (xj, yj, zj) and (xj, yj, zj+1). • Cv : wirelength cost of a via • Nl : the number of layers • P={p1, p2, …, pm} : a set of pins • O={o1, o2, …, ok} : a set of obstacles

9. PROBLEM FORMULATION(con’t) • SL-OARSMT, Nl = 1, is just a special case of ML-OARSMT. • Hence, we shall devise a unified algorithm to solve both SL- and ML-OARSMT problems.

10. Delaunay Triangulation

12. MST-Steiner

13. MST-Steiner

14. Obstacle-weighted MST Construction • op(pi, pj) : obstacle penalty • alpha is used to reflect the congestion of obstacles.

15. Rectilinearization & 3D U-shaped Pattern Refinement • Rectilinearization is performed on a three-dimensional escape graph based on Dijkstra’s shortest path algorithm. An escape graph introduces obstacles into the Hanan grid. • In addition, the segments intersecting obstacles are prohibited to be used. • If the processing edge has “zero” obstacle penalty, it can simply be rectilinearized by a monotonic pattern (L-shape or zigzag).

16. Rectilinearization & 3D U-shaped Pattern Refinement(con’t) • all 3D U-shaped patterns fall into two types: • (1) standard U-shape, and • (2) degenerated U-shape.

17. Rectilinearization & 3D U-shaped Pattern Refinement(con’t)

18. Compare

19. Compare(con’t)