Algorithms for VLSI Design Automation by Sabih H. Gerez

By Sabih H. Gerez

Modern microprocessors akin to Intel's Pentium chip commonly include thousands of transitors. identified generically as Very Large-Scale built-in (VLSI) structures, the chips have a scale and complexity that has necessitated the improvement of CAD instruments to automate their layout. This e-book specializes in the algorithms that are the construction 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 phases of design.

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11 A pseudo-code description of the breadth-first o w edges processed (ur) Ul e1 (uz, ul) u2 e3: (q' U3 ua, u5) (u+, us) (us) u4 : (v1, u2), e2 (u2, u4), e5 - search algorithm bf s. 9(a). 34 Algorithms for VLSI Design Automation edges processed determine the vertices added to the queue. From the figure it can be concluded that the vertices are visited in the order ut, uz, u3, u4, u5 while the edges are visited in the order et, e2, e3, e5 and e4. 1 it was mentioned that depth-first search could be used to find all vertices connected to a specific vertex us e v of a graph G(v,E).

Using this data structure, the analysis of the time complexity of depth-first search is rather simple. It was already mentioned that each vertex is visited exactly once. Since the outgoing edges of a vertex are only visited when the vertex itself is visited, all edges are also visited exactly once (an edge is an outgoing edge of one vertex only). Assuming that the generic vertex and edge actions have a constant time complexity, this leads to a time complexity of O(n + lEl) for depth-first search, where n : lVl.

5). 5 BibliographicNotes Several books entirely dedicated to algorithmic graph theory are available. Examples are: [Gib85] and [McH90]. Many books that deal with algorithms in general pay attention to graph theory in one or more chapters. Examples are: [Sed88] (this book uses Pascal as the language to describe algorithms; a version of the same book that uses C also exists tsedg0l), [cor90] and [Mool]. In these last books one can also find more details about the implementation of a FIFO queue necessary 40 Algorithms for VLSI Design Automation for the implementation of breadth-first search.

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