tailieunhanh - Handbook of algorithms for physical design automation part 96

Handbook of Algorithms for Physical Design Automation part 96 provides a detailed overview of VLSI physical design automation, emphasizing state-of-the-art techniques, trends and improvements that have emerged during the previous decade. After a brief introduction to the modern physical design problem, basic algorithmic techniques, and partitioning, the book discusses significant advances in floorplanning representations and describes recent formulations of the floorplanning problem. The text also addresses issues of placement, net layout and optimization, routing multiple signal nets, manufacturability, physical synthesis, special nets, and designing for specialized technologies. It includes a personal perspective from Ralph Otten as he looks back on. | 932 Handbook of Algorithms for Physical Design Automation The earliest power ground network sizing work 5 6 takes special advantage of the tree topology of the power ground network typically used in early designs. Instead of restricting the voltage drop on every node in the P G network only the voltage drop from root to every leaf of the tree structure is constrained where the root corresponds chip power pad and the leaf corresponds to the power pin of each macro. In this work constant branch current constraints Iimax and Iimin are used to further reduce the total number of voltage and current constraints. Chowdhury proposes to solve the general nonlinear optimization problem Equation on a general graph topology in Ref. 50 . In this work both currents and voltages are treated as variables. Specifically the entire optimization procedure consists of two optimization stages. Assuming fixed branch currents and given wi pl R and Ri Vi1 Vi2 the first stage minimizes area a nonlinear function of each branch voltage Area f v liWi where ai pI subject to change of current direction constraints Vi1 Vi2 --------- 0 Ii the minimum width constraints V Ii wi min voltage IR drop constraints and current density constraints. This problem was converted into an unconstrained convex programming problem and was solved using the conjugate gradient method. The second stage assumes that all nodal voltages are fixed the objective function becomes area M i where ft V P-V . Constraints include changes of current directions minimum width constraints and Kirchoff s current law. This is a linear programming problem. Tan et al. 51 improves the above method by expanding the nonlinear objection function of the first-stage optimization problem using Taylor s expansion as follows n df v v 2 ai y i 0 i i g v f y v-v L-7T -L vi d V Vi v i i i i Instead of minimizing the nonlinear objective function Equation they minimize Equation which is a linear .