an o n log n path based obstacle avoiding algorithm for rectilinear steiner tree construction
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An O(n log n) Path-Based Obstacle-Avoiding Algorithm for Rectilinear Steiner Tree Construction. Chih -Hung Liu, Shih-Yi Yuan , and Sy -Yen Kuo and Yao- Hsin Chou Form DAC2009. Introduction. Problem Formulation. Flow. Local Refinement :. Critical Path Generation.

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an o n log n path based obstacle avoiding algorithm for rectilinear steiner tree construction

An O(n log n) Path-Based Obstacle-Avoiding Algorithm for Rectilinear Steiner Tree Construction

Chih-Hung Liu, Shih-Yi Yuan , and Sy-Yen Kuo

and Yao-Hsin Chou

Form DAC2009

slide4
Flow

Local Refinement:

Critical Path Generation

Obstacle-Avoiding Steiner Tree Construction

OARST Construction:

shortest path tree
Shortest path Tree

Multi-source SPTs are equivalent to a terminal forest of Lin’s OASG. Therefore, a terminal forest of Lin’s OASG can be constructed in O(n log n) time without constructing Lin’s OASG

But the bridge edges could be O( n^2 )

oarst construction
OARST Construction
  • Since all edges of the OAST are visible we can directly transform an edge of the OAST into L-shaped rectilinear edges.
  • Consider the overlap between different edge.
local refinement
Local Refinement
  • U-shape refinement
  • moving offset of a segment may depend on the nearest obstacle. But the nearest obstacle may be changed.
  • We should compute the nearest obstacle of a movable segment in O( n log n ) time.
slide17

moving a segment to touch an obstacle can be divided into two cases:

    • (1) touch the obstacle corners
    • (2) just touch the obstacle boundary.
slide18

[16] the segment dragging query problem:

  • Given a set of n points, pick a horizontal (vertical) segment and answer the first hit point when dragging the segment vertically (horizontally).
experimental result
Experimental Result

[6] is most effective O(n log n)-time method

[7] achieves the best solution quality in [5] [6] [7]

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