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


An o n log n path based obstacle avoiding algorithm for rectilinear steiner tree construction
Flow Rectilinear Steiner Tree Construction

Local Refinement:

Critical Path Generation

Obstacle-Avoiding Steiner Tree Construction

OARST Construction:


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

Lin’s OASG Construction Rectilinear Steiner Tree Construction


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


An o n log n path based obstacle avoiding algorithm for 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


An o n log n path based obstacle avoiding algorithm for 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.


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

  • [ 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]