1 / 16

Bounded Radius Routing

Bounded Radius Routing. Perform bounded PRIM algorithm Under ε = 0, ε = 0.5, and ε = ∞ Compare radius and wirelength Radius = 12 for this net. BPRIM Under ε = 0. Example Edges connecting to nearest neighbors = ( c,d ) and ( c,e ) We choose ( c,d ) based on lexicographical order

denver
Download Presentation

Bounded Radius Routing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Bounded Radius Routing • Perform bounded PRIM algorithm • Under ε = 0, ε = 0.5, and ε = ∞ • Compare radius and wirelength • Radius = 12 for this net Practical Problems in VLSI Physical Design

  2. BPRIM Under ε = 0 • Example • Edges connecting to nearest neighbors = (c,d) and (c,e) • We choose (c,d) based on lexicographical order • s-to-d path length along T = 12+5 > 12 (= radius bound) • First appropriate edge found = (s,d) Practical Problems in VLSI Physical Design

  3. BPRIM Under ε = 0 (cont) • Radius bound = 12 s-to-y path length along T edges connecting to nearest neighbors first feasible appr-edge ties broken lexicographically should be ≤ 12; otherwise appropriate used Practical Problems in VLSI Physical Design

  4. BPRIM Under ε = 0 (cont) Practical Problems in VLSI Physical Design

  5. BPRIM Under ε = 0 (cont) Practical Problems in VLSI Physical Design

  6. BPRIM Under ε = 0.5 • Radius bound = 18 s-to-y path length along T edges connecting to nearest neighbors first feasible appr-edge ties broken lexicographically should be ≤ 18; otherwise appropriate used should be ≤12 Practical Problems in VLSI Physical Design

  7. BPRIM Under ε = 0.5 (cont) Practical Problems in VLSI Physical Design

  8. BPRIM Under ε = 0.5 (cont) Practical Problems in VLSI Physical Design

  9. BPRIM Under ε = ∞ Radius bound = ∞ = regular PRIM Practical Problems in VLSI Physical Design

  10. BPRIM Under ε = ∞ (cont) Practical Problems in VLSI Physical Design

  11. Comparison • As the bound increases (12 → 18 →∞) • Radius value increases (12 →17 → 22) • Wirelength decreases (56 → 49 → 36) Practical Problems in VLSI Physical Design

  12. Bounded Radius Bounded Cost • Perform BRBC under ε = 0.5 • εdefines both radius and wirelength bound • Perform DFS on rooted-MST • Node ordering L = {s, a, b, c, e, f, e, g, e, c, d, h, d, c, b, a, s} • We start with Q = MST Practical Problems in VLSI Physical Design

  13. MST Augmentation • Example: visit a via (s,a) • Running total of the length of visited edges, S = 5 • Rectilinear distance between source and a,dist(s,a) = 5 • We see that ε · dist(s,a) = 0.5 · 5 < S • Thus, we reset S and add (s,a) to Q (note (s,a) is already in Q) Practical Problems in VLSI Physical Design

  14. MST Augmentation (cont) visit nodes based on L dotted edges are added Practical Problems in VLSI Physical Design

  15. Last Step: SPT Computation • Compute rooted shortest path tree on augmented Q Practical Problems in VLSI Physical Design

  16. BPRIM vs BRBC • Under the same ε = 0.5 • BPRIM: radius = 18, wirelength = 49 • BRBC: radius = 12, wirelength = 52 • BRBC: significantly shorter radius at slight wirelength increase Practical Problems in VLSI Physical Design

More Related