Given n points on a plane, a Rectilinear Steiner Minimal Tree (RSM T ) connects these points through some extra points called steiner points to achieve a tree with minimal total wire length. Taking blockages into account dramatically increases the problem complexity. It is extremely unlikely that an efficient optimal algorithm exists for Rectilinear Steiner Minimal Tree Construction with Rectilinear Blockages (RSM T RB). Although there exist some heuristic algorithms for this problem, they have either poor quality or expensive running time.In this paper, we propose an efficient and effective approach to solve RSM T RB. The connection graph we used in this approach is called spanning graph which only contains O(n) edges and vertices. An O(n log n) time algorithm is proposed to construct spanning graph for RSM T RB. The experimental results show that this approach can achieve a solution with significantly reduced wire length. The total run time increased is negligible in the whole design flow.

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Abstract-A floorplan can be defined as a rectangular dissection of the floorplan region. Simple and tight asymptotic bounds on the number of floorplans for different dissection structures help us to evaluate the size of the solution space of different floorplan representation. They are also interesting theoretically. However, only loose bounds exist in the literature. In this paper, we derive tighter asymptotic bounds on the number of slicing, mosaic and general floorplans. Consider the floorplanning of blocks. For slicing floorplan, we prove that the exact number is !(( 1) +1 2) =0 (3 + 8) 2 1 2 1 2 and the tight bound is 2( !2 2 543 1 5 ) [9]. For mosaic floorplan, we prove that the tight bound is 2( !2 3 4 ). For general floorplan, we prove a tighter lower bound of ( !2 3 4 ) and a tighter upper bound of ( !2 5 4 5 ).Index Terms-Asymptotic bounds, general floorplan, mosaic floorplan, slicing floorplan.

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