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An Introduction to VLSI Physical Design by Majid Sarrafzadeh

By Majid Sarrafzadeh

This article treats the actual layout of very huge scale built-in circuits progressively and systematically. It examines the layout challenge and the layout technique with the purpose of comparing the potency of automated layout structures via algorithmic research. The structure challenge is considered as a set of sub-problems which are separately solved successfully after which successfully mixed. Initially,the textual content studies VLSI expertise after which examines structure ideas and phone iteration thoughts.

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Other approaches for finding a ratio cut have been proposed . One of the more interesting approaches is based on the spectral method, which use eigenvalues and eigenvectors of the matrices derived from the netlist . Early studies link the spectral properties and the partition properties of the graph . The algorithm proposed in [123] establishes a connection between graph spectra and ratio cuts and proposes an algorithm for solving the ratio-cut problem based on the underlying spectral properties .

In one pass of the algorithm, find a module with maximum gain . , the second nonempty element in list A), from the second gain to the third, and so on (and similarly for list B) . Without loss of generality, assume this module is in A (it is being moved to B), and denote it by M; . Repeat the following for each hyperedge that is connected to M; . Let e a be one of the hyperedges that is connected to M, . Case 1 . If all modules of ea are in A (that is, right before moving M,) then the gain of all these modules will be increased by w(ea ) .

R 34 AN INTRODUCTION TO VLSI PHYSICAL DESIGN Recently, it was shown [162] that, in general, the weight of the edges cut by any bipartition in the graph is not equal to the weight of the hyperedges cut by the same bipartition in the hypergraph . However, the transformation can be done if the addition of dummy vertices and the use of positive and negative weights are allowed . For example, some CAD tools proceed as follows . In order to transform a hypergraph into a graph, each hyperedge is transformed into a complete graph.

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