14 cjsherwani 92 data structures and basic algorithms

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Unformatted text preview: erent Steiner trees constructed from a MST (a) (b) (c) (d) Hwang's Thm (76'): The ratio of the cost of a rectilinear MST to that of an optimal RST is no greater than 3/2. (e) Algorithms for VLSI Physical Design Automation 3.15 cjSherwani 92 Rectilinear Steiner Trees Given a set of points on the plane Determine a Steiner tree using only horizontal and vertical v1=(x1,y1) wires( lines) Manhattan distance: cost(v1,v2) =|x1-x2|+|y1-y2| v1=(x1,y1), v2=(x2,y2) v2=(x2,y2) Steiner points Draw a horizontal and a vertical line through each point. Need to consider only grid points as steiner points Prim-based algorithm: Grow a connected subtree by iteratively adding the closest points It gives 3/2-approximation, i.e. cost(T)≤3/2cost(Topt) Steiner Tree Heuristics Observation: MST ap...
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