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lec18-steiner

# dynamic programming approach note that d6 compute a

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Unformatted text preview: e MST Weight ω(i,j) of each edge is a 4-tuple w(i,j)= (dij, -|yi-yj|, -max(yi,yj), -max(xi,xj)) Weights are compared under lexicographic ordering j (xj,yj) dij i (xi,yi) Use Prim’s algorithm to compute a MST based on the weight function we obtain a rectilinear MST since the 1st component of w(i,j) is dij This MST is separable since the next three components in w(i,j) help break ties Run time O(n2) Compute an Optimal L-shaped Mapping Choose an arbitrary node as root Using dynamic programming Compute at each node v the following Φl(vi): min cost of Ti with (v,vi) using lower L-shape Φu(vi): min cost of Ti with (v, vi) using upper L-shape Ti Ti Compute an Optimal L-shaped Mapping (Cont’d) Φl(v) (or Φu(v) ) can be computed by examining 2d combinations of Φl(vi) and Φu(vi) (1≤i≤d) with (pv,v) taking upper (or lower) L pv pv v T1 T2 v Td T1 T2 Td Applying Spanning/Steiner Tree Algorithms General cell design: channel intersection graphs Standard cell/Gate array/Sea-of-gate design rectilinear steiner/spanning trees or grid graphs...
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