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ABSTRACT1 In this paper, we present an efficient method to solve the obstacleavoiding rectilinear Steiner tree problem optimally. Our work is developed based on the GeoSteiner approach, modified and extended to allow rectilinear blockages in the routing region. We extended the proofs on the possible topologies of full Steiner tree (FST) in [4] to allow blockages, where FST is the basic concept used in GeoSteiner. We can now handle hundreds of pins with multiple blockages, generating an optimal solution in a reasonable amount of time. This work serves as a pioneer in providing an optimal solution to this difficult problem.

Abstract-Power consumption has become a crucial problem in modern circuit design. Multiple supply voltage (MSV) design is introduced to provide higher flexibility in controlling the power and performance tradeoff. One important requirement of MSV design is that timing constraints of the circuit must be satisfied after voltage assignment of the cells. In this article, we develop two algorithms to solve the voltage assignment problem under timing constraints, namely, min-cost flow (MCF) and valueoriented branch-and-bound (VOBB). In the MCF algorithm, the voltage assignment problem is formulated as a convex cost dual network flow problem, and can be solved optimally in polynomial time under certain conditions by calling a MCF solver. The VOBB algorithm, which is a VOBB-based searching method, solves the voltage assignment problem optimally in general cases by employing the MCF algorithm and a linear programming solver as subroutines. At last, we propose a MSV-driven floorplanning framework that optimizes power consumption and physical layout of a circuit simultaneously during the floorplanning stage, by embedding the MCF algorithm into a simulated annealingbased floorplanner and applying the VOBB algorithm as a postprocessing step. We compared our approach with the latest works on this problem, and the experimental results show that, using our approach, significant improvement on power saving can be achieved in much less running time, which confirms the effectiveness and efficiency of our method.

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