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Additional info for Combinatorial Algorithms for Integrated Circuit Layout

Sample text

The routing on each layer is planar, that is, no wires cross (courtesy Nixdorf Computer AG). Chapter 1. Introduction to Circuit Layout 28 y y --- .. 15: Variants of sizing functions for cells. (a) A fixed cell that cannot be rotated (with just one layout alternative; namely, the dashed rectangle indicated in the figure). (b) The same cell as in (a), but this time the cell can be rotated. (c) A cell with a finite number of layout alternatives. (d) A cell with an infinite number of layout alternatives.

15 shows several alternatives for sizing functions. Floorplanning now chooses a good layout alternative for each block and pieces together a good placement for the resulting cells. Like placement, floorplanning partly relies on inaccurate data. In floorplanning, in addition to the inaccuracy of the cost functions that we optimize, the area requirements for the cells may be inaccurate. As we move down the hierarchy, it may turn out that some cells need more area than we allocated for them, and that others need less.

T(A, p) E 7r(p) . - p,l(p)=n If there are just a few hard instances of a given length, and these instances are unlikely to occur, they will not appreciably affect the average-case complexity of the algorithm. Thus, if we know the probability distribution of the problem instances, average-case complexity is a more realistic complexity measure than is worst-case complexity in many situations. The average-case complexity measure has two disadvantages. The first is that it is quite difficult to determine the average-case complexity of an algorithm, even for simple probability distributions.

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