A practical detailed placement algorithm under multi-cell spacing constraints

Cheng, Yu-Hsiang; Huang, Ding‐Wei; Mak, Wai-Kei; Wang, Ting-Chi

doi:10.1145/3240765.3240772

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…Many other authors, therefore, settle for a dynamic programming solution instead of generalizing the Clumping Algorithm, guaranteeing a reasonable runtime by artificially bounding the maximum displacement allowed for each cell by a small number of placement sites. In exchange, they show how to make their dynamic program aware of several other desirable objective traits or incorporate a larger degree of freedom by allowing for a local reordering of cells, even between multiple rows [6], [11], [12], [19]. Other approaches comprise solving a linear complementarity problem to approximately minimize the squared cell movement and then resolving the remaining overlaps [5], [18], [25], applying integer linear programming to legalize sufficiently small regions of the chip separately [14], or making use of a cell insertion scheme [7], combined with bipartite matching and min-cost-flow-algorithms [17].…”

Section: Introductionmentioning

confidence: 99%

A Fast Optimal Double Row Legalization Algorithm

Hougardy¹,

Neuwohner²,

Schorr³

2021

Preprint

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In Placement Legalization, it is often assumed that (almost) all standard cells possess the same height and can therefore be aligned in cell rows, which can then be treated independently. However, this is no longer true for recent technologies, where a substantial number of cells of double-or even arbitrary multiple-row height is to be expected. Due to interdependencies between the cell placements within several rows, the legalization task becomes considerably harder. In this paper, we show how to optimize quadratic cell movement for pairs of adjacent rows comprising cells of single-as well as double-row height with a fixed left-to-right ordering in time O (𝑛 • log(𝑛)), whereby 𝑛 denotes the number of cells involved. Opposed to prior works, we thereby do not artificially bound the maximum cell movement and can guarantee to find an optimum solution. Experimental results show an average percental decrease of over 26% in the total quadratic movement when compared to a legalization approach that fixes cells of more than single-row height after Global Placement. CCS CONCEPTS• Hardware → Placement.

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