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Algorithms for VLSI Design Automation by Sabih H. Gerez

By Sabih H. Gerez

Modern microprocessors resembling Intel's Pentium chip more often than not include thousands of transitors. recognized 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 structure of VLSI circuits. one of many first books at the topic, this consultant covers all levels of design.

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L7 The pseudo-code description of Prim's minimum spanning tree algorithm. being constructed as well as the final spanning tree are graphs. Their vertex and edge sets are represented by the variables I4u and F respectively. Here again, the data structures used are left vague intentionally. Even the use of separate records for vertices and edges is not necessarily required. They are only mentioned in order to be able to deal with abstract sets of vertices and edges. Besides, it is assumed that a vertex has the attributes distance and via-edge.

In the main program, the function is applied to each vertex of the graph to account for the fact that not all vertices may be reachable from a single vertex. An adjacencyJist representation is appropriate in this situation as it gives direct access to the outgoing edges ofeach vertex. 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).

2 (b) An instance of the graph version of rSp (a) and an oprimal solution (b). Example: the optimization version of the shortest-path problem in graphs requires that the edges forming the shortest path are identified, whereas the evaluation version merely asks for the length of the shortest path. For mathematical reasons, the theory of Np-completeness only deals with socalled decision problems. These are problems that only have two possible answers: "yes" or "no"' This is not a serious restriction, as far as combinatorial optimization problems are concerned.

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