1 / 14

Parallel Computational Geometry

visibility lower envelope union of rectangles 3-D convex hull and 2-D Voronoi Diagram. CGM complexity: O(1) rounds O(T s (n) / p) local computation n/p > p. Parallel Computational Geometry. Lower Envelope. Given: A set S of n non-intersecting line segments. S. Lower Envelope.

landers
Télécharger la présentation

Parallel Computational Geometry

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. visibility lower envelope union of rectangles 3-D convex hull and 2-D Voronoi Diagram ... CGM complexity: O(1) rounds O(Ts(n) / p) local computation n/p > p ParallelComputational Geometry

  2. Lower Envelope • Given: A set S of n non-intersecting line segments S

  3. Lower Envelope • Given: A set S of n non-intersecting line segments S LE(S) • Task: Compute the lower envelope LE(S)

  4. Lower Envelope • Goal: O(1) rounds • Problem: Each processor “sees” only O(n/p) line segments

  5. Lower Envelope proc. 1 proc. 2 proc. 3 proc. 4 S1 S2 S3 S4 S = S1S2S3S4

  6. Lower Envelope proc. 1 proc. 2 proc. 3 proc. 4 S1 S2 S3 S4 S = S1S2S3S4 • Step 1: Each proc. Pi computes locally LE(Si)

  7. Lower Envelope proc. 1 proc. 2 proc. 3 proc. 4 S1 S2 S3 S4 S = S1S2S3S4 • Step 1: Each proc. Pi computes locally LE(Si) proc. 1 proc. 2 proc. 3 proc. 4

  8. Lower Envelope • Step 2: Globally sort [i=1..pLE(Si)] by x-coord. of right endpoint

  9. Lower Envelope • Step 2: Globally sort [i=1..pLE(Si)] by x-coord. of right endpoint proc. 1 proc. 2 proc. 3 proc. 4 V1 V2 V3 V4

  10. Lower Envelope • Step 3: Each Pi determines Li and broadcasts Li to all other Pj (one h-relation) proc. 1 proc. 2 proc. 3 proc. 4 V1 V2 V3 V4 L1 L2 L3 L4

  11. Lower Envelope • Step 4: Each Pi scans LE(Si) and sends the segment intersecting Lj to Pj for j=1..p (one h-relation) proc. 1 proc. 2 proc. 3 proc. 4 R1 R2 R3 R4 V1 V2 V3 V4 L1 L2 L3 L4

  12. Lower Envelope • Step 5: Each Pi computes LE(Vi Ri) proc. 1 proc. 2 proc. 3 proc. 4 R1 R2 R3 R4 V1 V2 V3 V4 L1 L2 L3 L4

  13. Lower Envelope

More Related