An Introduction To VLSI Physical Design by Majid Sarrafzadeh

By Majid Sarrafzadeh

This article bargains insurance of actual layout stream and present VLSI layout technique. It covers performance-driven layout, multi-chip module (mcm) expertise and FPGAs. every one bankruptcy has workout sections - one on recommendations, the opposite on machine programming.

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The running time of the ratio-cut algorithm is 0(1EI) time. Proof. Examine the time complexity of each phase separately . In the initialization step, randomly find a node s . Node t (the node farthest from s) can be obtained by breadth-first search in O (I E I) time . There are two lists, list A and list B, to store nodes in X and Y, respectively . As in the Fiduccia-Mattheyses algorithm, each list is indexed by the set [-dmax • Wmax, dmax • wmax] . As before, dm ax is the maximum vertex degree in the graph, and Wmax is the maximum cost of an edge .

U„} and B is the set of bins, B = {bi, bz, . , b k} . The weight wi , ; of an edge connecting one vertex u, in U and one vertex b; in B is set to s(u,), where s(u,) is the size of item u i . The objective is to maximize E (i )EE (wi,jxi,j), subject to the following four constraints : (1) (2) (3) (4) I I [0,1] constraint : x i , j E {0, 1}, capacity constraint: >(w,, ;xi , ; : Vi E U) < b,, Vj E B, assignment constraint: Y(xi, ; : Vi E B) = 1, Vi E U . completeness constraint : the total number of x,, ; s whose value is 1 is equal to n .

Algorithms for optimization problems go through a number of steps . At each step, a choice, or a set of choices, is made . In greedy algorithms the choice that results in a locally optimal solution is made . Typically, greedy algorithms are simpler than other classes of algorithms . However, they do not always produce globally optimal solutions . Even if they do, it is not always an easy task to prove them . • Dynamic programming . A problem is partitioned into a collection of subproblems, the subproblems are solved, and then the original problem is solved by combining the solutions .

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