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

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 Rectilinear Steiner Tree Construction

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 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 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 Rectilinear Steiner Tree Construction

Critical Path Generation: Rectilinear Steiner Tree Construction

OAST Construction Rectilinear Steiner Tree Construction

Use Heap maintain the edge weight Rectilinear Steiner Tree 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 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.

- moving a segment to touch an obstacle can be divided into Rectilinear Steiner Tree Constructiontwo cases:
- (1) touch the obstacle corners
- (2) just touch the obstacle boundary.

- [ 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 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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