Design automation and analysis of three-dimensional integrated circuits

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 165-176).This dissertation concerns the design of circuits and systems for an emerging technology known as three-dimensional integration. By stacking individual components, dice, or whole wafers using a high-density electromechanical interconnect, three-dimensional integration can achieve scalability and performance exceeding that of conventional fabrication technologies. There are two main contributions of this thesis. The first is a computer-aided design flow for the digital components of a three-dimensional integrated circuit (3-D IC). This flow primarily consists of two software tools: PR3D, a placement and routing tool for custom 3-D ICs based on standard cells, and 3-D Magic, a tool for designing, editing, and testing physical layout characteristics of 3-D ICs. The second contribution of this thesis is a performance analysis of the digital components of 3-D ICs. We use the above tools to determine the extent to which 3-D integration can improve timing, energy, and thermal performance. In doing so, we verify the estimates of stochastic computational models for 3-D IC interconnects and find that the models predict the optimal 3-D wire length to within 20% accuracy. We expand upon this analysis by examining how 3-D technology factors affect the optimal wire length that can be obtained. Our ultimate analysis extends this work by directly considering timing and energy in 3-D ICs. In all cases we find that significant performance improvements are possible. In contrast, thermal performance is expected to worsen with the use of 3-D integration. We examine precisely how thermal behavior scales in 3-D integration and determine quantitatively how the temperature may be controlled during the circuit placement process. We also show how advanced packaging(cont.) technologies may be leveraged to maintain acceptable die temperatures in 3-D ICs. Finally, we explore two issues for the future of 3-D integration. We determine how technology scaling impacts the effect of 3-D integration on circuit performance. We also consider how to improve the performance of digital components in a mixed-signal 3-D integrated circuit. We conclude with a look towards future 3-D IC design tools.by Shamik Das.Ph.D

High-Quality Hypergraph Partitioning

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time

Partitioning by Iterative Deletion

Netlist partitioning is an important and well studied problem. In this paper, a linear time partitioning approach based on iterative deletion is presented. We use the partitioning problem to allow a fair comparison of the iterative deletion approach with well known iterative improvement methods. For partitioning problems with a range of edge weights, and for multi-way partitioning, the iterative deletion approach can outperform the iterative improvement method. The algorithmic approach is flexible and can support complex cost functions directly. 1