TAILIEUCHUNG - Handbook of algorithms for physical design automation part 9

Handbook of Algorithms for Physical Design Automation part 9 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. | 62 Handbook of Algorithms for Physical Design Automation new item is equal to the finished item with its p value incremented by the p value of the other current item. The idea of the max-plus list is to finish a sublist of more than one item at one iteration. Assume that At m Bj m we want to find a i k a such that Ak m Bj m but Ak 1 m Bj m. These items At . Ak are finished and put into the new list after their p values are incremented by Bj p. The speedup over Stockmeyer s algorithm comes from the fact that this sublist is processed identified and updated in a batch mode instead of item by item. The forward pointers in a max-plus list are used to skip items when searching for the sublist and an adjust field is associated with each forward pointer to record the incremental amount on the skipped items. Each item is defined by the following C code struct maxplus_item int level the level float m p the two values float adjust struct maxplus_item forward forward pointers The size of adjust array is equal to the level of this item and adjust i means that the p values of all the items jumped over by forward i should add a value of adjust i . Two skip lists with sizes q and r q r can be merged in O q qlog r q expected time 18 . This quantity is proportional to the number of jump operations performed on the skip list. Max-plus lists are merged in a similar manner except that the adjust field need to be updated. The complexity is also proportional to the number of jump operations. However it can be shown that the number of jump operations in a maxplus merge is within a constant facor of the number of jumps in an ordinary skip list. Thus the expected complexity of a max-plus merge is identical to that of a skip-list merge which is the same as that of a balanced binary search tree. LAYOUT DATA STRUCTURES Transistors and logic gates are manufactured in layers on silicon wafers. Silicon s conductivity can be significantly improved by diffusing n- and p-type dopants into it. .

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