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


Introduction
Introduction Rectilinear Steiner Tree Construction


Problem formulation
Problem Formulation Rectilinear Steiner Tree Construction


Flow Rectilinear Steiner Tree Construction

Local Refinement:

Critical Path Generation

Obstacle-Avoiding Steiner Tree Construction

OARST Construction:


Lin’s OASG Construction Rectilinear Steiner Tree Construction


Long s mtst algorithm
Long’s MTST algorithm Rectilinear Steiner Tree Construction


MTST of Rectilinear Steiner Tree ConstructionLin’s OASG is an OARSMT for any two-pin net or multiple-pin nets where an OARSMT


Shortest path tree
Shortest path Tree Rectilinear Steiner Tree Construction

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 )


Shortest path map
Shortest Path Map Rectilinear Steiner Tree Construction


Critical path generation
Critical Path Generation: Rectilinear Steiner Tree Construction


Proof sol of cps mtst of oasg
Proof: Sol of CPs Rectilinear Steiner Tree Construction≈ MTST of OASG

V1

V4

V2

P1

P2

V3

P3


Oast construction
OAST Construction Rectilinear Steiner Tree Construction


Use Heap maintain the edge weight Rectilinear Steiner Tree Construction


Oarst construction
OARST Construction Rectilinear Steiner Tree 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 Rectilinear Steiner Tree Construction

  • 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.



  • [ Rectilinear Steiner Tree Construction16] 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 Rectilinear Steiner Tree Construction

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

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


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