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see also Partitioning KLFM algorithm, 841. Kou, Markowsky, and Berman (KMB) method, 494 Kraftwerk Kruskal’s algorithm, 59, 79–80. updating of dual parameters, 97 Lam’s algorithm, 314. Lee’s algorithm, 476 Lee’s router. see also Mathematical partitioning formulations Linear programming problem Linear program/programming . see also Multiscale optimization, in placement Logic array blocks (LABs), 945. partitioning-based placement techniques Capo, 308. Modeling defect,...
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Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C000 Finals Page i . Handbook of. Algorithms for. Physical design. Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C000 Finals Page iii . Handbook of algorithms for physical design automation / edited by Charles J. Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C000 Finals Page v . Alpert/Handbook of Algorithms for Physical Design...
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Chapter 40 X Architecture Place and Route: Physical Design for the X Interconnect. Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C000 Finals Page xi . PART X Physical Design for Specialized Technologies. Chapter 47 Physical Design for Three-Dimensional Circuits. Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C000 Finals Page xiii . He received two undergraduate degrees from Stanford University in...
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1 Introduction to Physical Design. 1.2 Overview of the Physical Design Process. 1.3 Overview of the Handbook. The purpose of VLSI physical design is to embed an abstract circuit description, such as a netlist, into silicon, creating a detailed geometric layout on a die. In the early years of semiconductor technology, the task of laying out gates and interconnect wires...
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Also a net ordering strategy has to be determined, mostly to achieve close to full wire list completion. And taking into account sufficient effects of modern technology (e.g., cross talk, antenna phenomena, metal fill, lithography demands) makes router design a formidable task, today even more than in the past. Placement is initially seen as an assignment problem where n modules...
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Nevertheless, it is the structure of the local minima. The introduction of the fruits of design automation of the 1980s in industry generated mostly distrust and disbelief among designers. Yet, there was a solid background in algorithms and heuristics, and a better understanding of the problem and its context. Many of the original approaches were revisited, improved and, above all,...
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FIGURE 3.3 Elmore delay: approximating the median with the mean.. Another important characteristic is the median, which is defined as the halfway point on a PDF curve:. Observe that the commonly used 50 percent delay point in circuit analysis actually corresponds to the median of the underlying distribution. This is the keen observation of Elmore in 1948. 3.1.1.2 Elmore Delay...
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Coupling noise is yet another unwanted side effect of the scaling in deep submicron technology, and its impact can be reduced through physical design transformations. On the other hand, because the chip size is also getting larger (in terms of multiples of the minimum feature size), it is necessary to reduce wire resistance by increasing the aspect ratio of the...
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Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C003 Finals Page . 52 Handbook of Algorithms for Physical Design Automation. In Proceedings of the IEEE Custom Integrated Circuits Conference, San Jose, CA, pp. A critical examination of the mechanics of dynamic NBTI for pMOSFETs. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, San Jose, CA, pp. In Proceedings of...
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new item is equal to the finished item with its p value incremented by the p value of the other current item. The idea of the max-plus list is to finish a sublist of more than one item at one iteration. The complexity is also proportional to the number of jump operations. However, it can be shown that the number...
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5.4.2.1 Kruskal’s Algorithm. 5.4.2.2 Prim’s Algorithm. 5.4.3.1 Dijkstra’s Algorithm. The chapter begins by discussing ways of analyzing the complexity of algorithms, fol- lowed by general algorithmic concepts like greedy algorithms and dynamic programming. The chapter ends with the description of the technique of simulated annealing.. An algorithm is essentially a sequence of simple steps used to solve a complex problem....
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If an edge does not exist in the network then its capacity is set to zero.. Definition 6 A flow in the network G is a real value function f : VXV → R. The value of a flow is typically defined as the amount of flow coming out of the source to all the other nodes in the network....
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subject to f i ( x. The optimization problem (Equation 6.1) is said to be convex if (1) the functions f i ( i = 0, 1, 2. (2) h j ( x ) are affine functions (i.e., h j is of the form a T j x + b j for some a j ∈ n and b j....
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For circuit design applications, we often encounter optimization problems with design variables corresponding to the geometry of the circuit. An example of a geometric program in the context of physical design is described in Chapter 29.. 5x 1 2.3 x 2 −0.7 x 3 2.5 is a monomial. A GP is an optimization problem in the form. In this original...
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To cut off one vertex from the rest requires cutting three edges, so the weight should be 1/3 (for a total edge weight of 1). However, to cut off two vertices from the rest requires cutting four edges (each with weight 1/4). Because some of the edges assigned weights of 1/3 and 1/4 may be the same, this weighting scheme...
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FIGURE 7.9 Placements of prim1 using (a) two eigenvectors and (b) three eigenvectors.. It is also possible to use multiple eigenvectors to determine arrangements of vertices that minimize the number of cuts. Hall [Hal70] suggests that the location of the vertices in r-dimensional space can be used to identify blocks (see Section 7.3.1 for a description of his method). The...
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The novelty of this technique lies in the way the blocks are determined.. Multilevel methods have proven to be the partitioning technique of choice in the VLSI community owing to the quality of results they produce with very small runtimes. Markov, Hypergraph partitioning with fixed vertices, IEEE Transactions on Computer-Aided Design of Circuits and Systems . Kahng, A hybrid multilevel/genetic...
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FIGURE 8.2 (a) Rectangular graph N , (b) its geometric dual without the vertex for the exterior face, (c) its inner dual, and (d) its rectangular dual. duals for a given R, the strength of the dualization method lies in the fact that a solution, if one exists, can nevertheless be found in linear time [14].. Hence, a rectangular graph...
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As part of the macrocell based layout system called BEAR, the hierarchical floorplanner by Dai et al. For each cluster, the shapes of the blocks are also considered so that there is no mismatch within the cluster. Issues with size incompatibility at higher levels between two neighboring clusters with fewer connections may arise, but these can be resolved by limiting...
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FIGURE 9.1 Slicing floorplan and its two slicing trees. Figure 9.1a shows a slicing floorplan for four modules. Moreover, the shape flexibilities of modules can be fully utilized to pack modules tightly [3–5]. In the floorplan design problem, we are given a set of n modules, named 1, 2. For each module i. specifies the set of modules with free...