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1995 | Buch

On Optimal Interconnections for VLSI

verfasst von: Andrew B. Kahng, Gabriel Robins

Verlag: Springer US

Buchreihe : The International Series in Engineering and Computer Science

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Über dieses Buch

On Optimal Interconnections for VLSI describes, from a geometric perspective, algorithms for high-performance, high-density interconnections during the global and detailed routing phases of circuit layout. First, the book addresses area minimization, with a focus on near-optimal approximation algorithms for minimum-cost Steiner routing. In addition to practical implementations of recent methods, the implications of recent results on spanning tree degree bounds and the method of Zelikovsky are discussed. Second, the book addresses delay minimization, starting with a discussion of accurate, yet algorithmically tractable, delay models. Recent minimum-delay constructions are highlighted, including provably good cost-radius tradeoffs, critical-sink routing algorithms, Elmore delay-optimal routing, graph Steiner arborescences, non-tree routing, and wiresizing. Third, the book addresses skew minimization for clock routing and prescribed-delay routing formulations. The discussion starts with early matching-based constructions and goes on to treat zero-skew routing with provably minimum wirelength, as well as planar clock routing. Finally, the book concludes with a discussion of multiple (competing) objectives, i.e., how to optimize area, delay, skew, and other objectives simultaneously. These techniques are useful when the routing instance has heterogeneous resources or is highly congested, as in FPGA routing, multi-chip packaging, and very dense layouts.
Throughout the book, the emphasis is on practical algorithms and a complete self-contained development. On Optimal Interconnections for VLSI will be of use to both circuit designers (CAD tool users) as well as researchers and developers in the area of performance-driven physical design.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Preliminaries
Abstract
This book discusses problems of “optimal interconnection” and describes efficient algorithms for several basic formulations. Our domain of application is the computer-aided design (CAD) of very large-scale integrated (VLSI) circuits, wherein interconnection design is now one of the most actively studied areas. However, much of what we develop can be applied to other domains ranging from urban planning to the design of communication networks. Because most formulations that we study are intractable, the term “optimal” in some sense is a misnomer: rather, our focus is on the reasoned and principled development of good heuristics.
Andrew B. Kahng, Gabriel Robins
Chapter 2. Area
Overview
To achieve a minimum-area layout, circuit interconnections should in general be realized with minimum total wirelength. This chapter discusses the corresponding Steiner minimal tree (SMT) problem, which seeks to connect a given set of points in the plane using the minimum amount of wiring. The SMT problem is central to VLSI global routing and wiring estimation; it also arises in such non-VLSI applications as communication network design. Recent reference books treat the Steiner problem in detail [138, 139]. Thus, in this chapter we will limit our discussion to the rectilinear SMT formulation, which reflects the Manhattan geometry of VLSI layout. The discussion focuses on an iterative construction, called Iterated 1-Steiner, that eschews traditional analogies to minimum spanning tree solutions. Practical implementation issues are discussed as well.
Our development will be as follows. We first demonstrate that many existing SMT heuristics have a performance ratio of 3/2 in the Manhattan plane, which is the same bound achieved by the minimum spanning tree (MST) construction. We then develop the Iterated 1-Steiner (I1S) heuristic, an iterative construction that can achieve good performance even on inputs that are pathological for previous methods. For uniform distributions of 8-point instances in the plane, I1S obtains solution costs that are optimal for 90% of uniformly distributed instances, and average within 0.25% of optimal overall. (The I1S approach also applies to graph instances and higher-dimensional geometric instances.) We present a straightforward implementation of I1S, along with a parallel implementation that achieves near-linear speedup. Similarities between I1S and the recent method of Zelikovsky are also discussed. Finally, we show that any pointset in the Manhattan plane has an MST with maximum degree 4, and that in three-dimensional Manhattan space the maximum MST degree is 14 (the best previous bounds were 6 and 26, respectively): this result improves I1S runtimes and is of independent theoretical interest. The chapter concludes with a discussion of the Steiner problem in graphs.
Andrew B. Kahng, Gabriel Robins
Chapter 3. Delay
Abstract
This chapter considers the problem of minimizing signal delay for performance-driven system design. The signal delay objective moves us from the unoriented pointset P of the Steiner problem to an oriented signal net S which has an identified source. Optimal-delay wiring geometries can differ substantially from those of optimal-area (Steiner minimal tree) solutions, particularly as technology moves into submicron regimes and layout dimensions continue to increase. Our discussion reflects the history of our recent research, which has addressed four major issues.
Andrew B. Kahng, Gabriel Robins
Chapter 4. Skew
Abstract
The heart of a digital system is its clock, which is the control signal that synchronizes the flow of data among functional elements. To achieve maximum system performance, it is necessary to limit the clock skew, i.e., the maximum difference in arrival times of the clock signal at synchronizing elements (sequential registers, or clock sinks) of the design. This has been idealized in the recent literature as the “zero-skew clock routing problem”, which seeks a routing tree that delivers the synchronizing clock pulse from its source to all clock sinks simultaneously. At the same time, the cost of the clock routing tree must be minimized in light of system power requirements, signal integrity, and area utilization. This chapter views clock tree construction to minimize skew and tree cost as a combination of two processes — topology generation and geometric embedding — and presents methods which accomplish each of these processes using either linear delay or Elmore delay to guide the construction. Our focus is on the sequence of recent works by Jackson et al. [143], Kahng et al. [144], Tsay [240], Boese et al. [29] Chao et al. [44, 45], Edahiro [82, 84], Zhu and Dai [259], and Kahng and Tsao [153] which lead to the present state of single-layer, exact zero-skew clock tree constructions.
Andrew B. Kahng, Gabriel Robins
Chapter 5. Multiple Objectives
Overview
In previous chapters we have explored constructions that optimize the three main design objectives of wirelength, skew, and delay. However, in practice we often seek to optimize multiple objectives simultaneously. This chapter explores ways of representing and addressing multiple competing objectives. We begin with a minimum density formulation for balancing the utilization of horizontal and vertical routing resources and describe heuristics with expected performance bounded by constants times optimal. This enables the simultaneous optimization of up to three objectives (e.g., radius/density/wirelength, or skew/density/wirelength at once), without degrading solution quality with respect to any of the objectives. We also discuss a non-uniform lower bound schema that affords tighter estimates of solution quality for a given problem instance.
Next, we develop a general framework of multiple-objective optimization, based on multi-weighted graphs (i.e., where edge weights are vectors rather than scalars). This formulation captures distinct criteria such as wirelength, jogs and congestion, and enables effective routing in graph-based regimes (i.e., routing in building-block designs, field-programmable gate arrays, and where obstacles are present). Finally, we discuss a network-flow based approach to prescribed-width routing where multiple objectives induce an arbitrarily costed region; applications of this include, e.g., circuit-board routing, and routing with respect to reliability or thermal considerations. This methodology departs from conventional shortest-path or graph-search based methods in that it applies to routing regions with a continuous cost function, as well as to regions containing solid polygonal obstacles. Extensions address the minimum-surface problem of Plateau, which is of independent interest.
Andrew B. Kahng, Gabriel Robins
Backmatter
Metadaten
Titel
On Optimal Interconnections for VLSI
verfasst von
Andrew B. Kahng
Gabriel Robins
Copyright-Jahr
1995
Verlag
Springer US
Electronic ISBN
978-1-4757-2363-2
Print ISBN
978-1-4419-5145-8
DOI
https://doi.org/10.1007/978-1-4757-2363-2