E costt32costtopt steiner tree heuristics observation

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Unformatted text preview: proximation can be easily improved cost(T)=6 cost(T)=4 Difficulty: where to add Steiner points?? L-Shaped MST approach Ho, Vijayan and Wong, “ A new approach to the rectilinear steiner tree problem”, DAC’89, pp161-166 Basic Idea: Each on-degenerated edge in MST has two possible L-shaped layouts, choose one for each edge in MST to maximize overlap. degenerate edges MST non-degenerate edge two L-shaped layouts one L-shaped mapping Problem: Compute the best L-shaped mapping another L-shaped mapping Key Ideas in L-RST Approach Separable MST: bounding boxes of every two nonadjacent edges don’t intersect or overlap non-separable MST separable MST Theorem: Every point set has a separable MST Theorem: Each node is adjacent to at most 8 edges (6 non-degenerate edges) in a rectilinear MST Theorem: We can compute an optimal L-shaped implementation of an MST in O(2d•n) time. ( Dynamic Programming Approach). Note that d≤6 Compute a Separabl...
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