TAILIEUCHUNG - Handbook of algorithms for physical design automation part 44

Handbook of Algorithms for Physical Design Automation part 44 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. | 412 Handbook of Algorithms for Physical Design Automation Tetris-Based Legalization Rather than distributing logic elements with flow-like methods an alternate approach based on packing is possible. The Tetris legalization method by Hill 12 is remarkably simple and trivial to implement. We first discuss the approach in the context of standard cell design and then show how it extends to handle a mix of standard cells and macroblocks. For each cell c we have a desired position x y the cells must be legalized into standard cell rows R r1 r2 . rk and assume that the left-most open position in each row is known. The legalization method first sorts the cells C by their x position and then inserts them into the left side of a row in a greedy manner such that the displacement of each cell is minimized. Algorithm 4 The Tetris legalizer by Hill C All cells to be legalized Sort the cells in C by their X-coordiates to get Ls lj left-most position of each row rj for i 1 to the number of cells do best lim sup for j 1 to the number of rows do cost displacement of moving cell i in Ls to lj if cost best then best cost best_row j end if end for Move cell i in Ls to the row best_row lbest_row lbest_row widthi end for Pseudocode for the approach is shown in Algorithm 4. If one were to rotate the placement region counterclockwise the legalization process might look very much like a game of Tetris for which the algorithm is named. Our example code can be made to run more quickly by only considering rows close to the desired position of a cell in practice runtimes are linear with the number of cells to be legalized. Our example also packs cells to the left but this is not in general necessary if space has been reserved for routability it may be perferable to legalize into a position that is not to the left. Other obvious variants are to legalize from both the left and right sides and to sort the cells by their leftmost boundary rather than their center. The method can also be .

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