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By Sabih H. Gerez

Modern microprocessors similar to Intel's Pentium chip mostly include hundreds of thousands of transitors. recognized generically as Very Large-Scale built-in (VLSI) platforms, the chips have a scale and complexity that has necessitated the improvement of CAD instruments to automate their layout. This ebook makes a speciality of the algorithms that are the development blocks of the layout automation software program which generates the format of VLSI circuits. one of many first books at the topic, this consultant covers all levels of design.

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The sets V and E fully characteize a graph. 1 shows a graph where V : lut,u2,u3,u4,u5,u6l and E : {et,ez,4,e4,e5}. The two vertices that are joined by an edge are called the edge's endpoints. An edge can be identif,ed by its two endpoints u, u € V, in which case the notation (u, u) is used. 1, e1 - @t,uz), e2 : (u1, u3), etc. When e : (u,u), it is said that e is incident with u (and also with u). The vertices u and u such that (u, u) e E, are called adjacent. When one removes vertices and/or edges from a given graph G, one gets a subgraph of G.

Like to edit a circuit with a schematic editor, simulate it with a tool of another vendor, go back to the schematics, simulate again, without having to bother about data conversion. This is possible if a framework is used. One of its features is a uniform interface to access design data from a database. Then all tools can exchange data by making use of standardized procedure calls to read from and write to the common database provided by the framework. A framework can also provide for uniform user interfaces using a similar mechanism of standardized procedure calls.

2 Data Structures for the Representation of Graphs If one wants to implement graph algorithms, one of the first issues to be settled is how to represent the graph in a computer. In other words, one should choose a suitable data structure for graphs. There is no optimal data structure that should be used in all algorithms. Different algorithms have different requirements. One of the most straightforward ways to represent graphs is by means of an adjacency matrix. If the graph G(V,E) has r vertices, an r?

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