TAILIEUCHUNG - Handbook of algorithms for physical design automation part 52

Handbook of Algorithms for Physical Design Automation part 52 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. | 492 Handbook of Algorithms for Physical Design Automation next subsection discusses a batched variant of the I1S approach which offers runtime improvements in practice. Batched 1 -Steiner Variant Although a single 1-Steiner point may be found in O n2 time the required computational geometry techniques are complicated and not easy to implement. To address these issues a batched variant of I1S was developed 19 54 which amortizes the computational expense of finding 1-Steiner points by adding as many independent 1-Steiner points as possible in every round. The batched 1-Steiner B1S variant computes AMST P x for each candidate Steiner point x e H P . the Hanan grid candidate points . Two candidate Steiner points x and y are independent if AMST P x AMST P y AMST P x y that is introducing each of the two 1-Steiner points does not reduce the potential gain in MST cost relative of the other 1-Steiner point. Given pointset P and a set of Steiner points S each round of B1S greedily adds into S a maximal set of independent 1-Steiner points. Termination occurs when around fails to add any new Steiner points Figure . The total time required for each round is O n2 log n . In three dimensions I1S exploits a generalization of Hanan s theorem to higher dimensions 41 namely that there always exists an optimal Steiner tree whose Steiner points are selected from the O n3 intersections of all axis-orthogonal planes passing through points of P. The three-dimensional analog of Hwang s result suggests that the Steiner ratio . the maximum sMSr ratio for three dimensions is at most however this is only a conjecture and generalizing Hwang s theorem to dimensions three and higher is still an open problem. An example consisting of six points located in the middle of the faces of a rectilinear cube establishes that is a lower bound for the Steiner ratio in three dimensions. The I1S and B1S algorithms are highly parallelizable because each processor can independently compute .

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