Efficient ObstacleAvoiding Rectilinear Steiner Tree有效的避障的直线Steiner树.pptVIP

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Efficient ObstacleAvoiding Rectilinear Steiner Tree有效的避障的直线Steiner树.ppt

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unit1 Efficient Obstacle-Avoiding Rectilinear Steiner Tree Construction Outline Outline Introduction to OARSMT Problem Given a set of pins and a set of obstacles, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) Connect those pins, possibly through some Steiner points Use only vertical and horizontal edges Avoid running through any obstacle Have a minimal total wirelength Construction-by-Correction Approach Connection-Graph Based Approach Outline Problem Formulation An OARSMT Example Outline Flow of Algorithms Flow of Algorithms Spanning Graph Construction Properties of Our Spanning Graph (1/2) Our spanning graph guarantees a shortest path of any two vertices. Properties of Our Spanning Graph (2/2) Spanning Graph Construction – Example Flow of Algorithms Spanning Tree Construction Flow of Algorithms Rectilinear Spanning Tree Construction Transform slant edges into vertical and horizontal edges Longer edges are transformed first. Three cases for a slant edge e and its neighboring edge e’: Rectilinear Spanning Tree Construction – Example Flow of Algorithms OARSMT Construction (1/2) Overlapping edge removal OARSMT Construction (2/2) Properties of Our OARSMT Our OARSMT is an optimal solution for: Any 2-pin net Any 3-pin net without obstacles Any net whose topology of an optimal solution contains only simple paths Complexity Overall time complexity O(n3) in the worst case O(n2 lgn) for practical applications n: # of pin-vertices and corner-vertices Outline Experimental Settings The algorithm is compared with Shi et al., ASP-DAC-06 Feng et al., ISPD-06 Shen et al., ICCD-05 22 benchmark circuits classified into 3 categories 5 industrial test cases from Synopsys (ind1--ind5) 12 test cases used by Feng et al. (rc1--rc12) 5 random test cases generated by us (rt1--rt5) # of pin-vertices ranges from 10 to 1,000 # of obstacles ranges from 10 to 10,000 Experimental Results – Effectiveness Compared to previous works, our algorithm improves 4.72%, 2