From the Publisher:
This work covers all aspects of physical design. The book is a core reference for graduate students and CAD professionals. For students, concept and algorithms are presented in an intuitive manner. For CAD professionals, the material presents a balance of theory and practice. An extensive bibliography is provided which is useful for finding advanced material on a topic. At the end of each chapter, exercises are provided, which range in complexity from simple to research level.

Algorithms for VLSI Physical Design Automation

The current status of VLSI layout and directions for future research are addressed, with emphasis on the authors' own work Necessary terminology and definitions and, whenever possible, a precise formulation of the problems are provided Placement and floorplanning for both the sea-of-gates and building-block designs are examined The former emphasizes the connectivity specification, whereas the latter must also consider module shape and size Global routing based on a method of successive cuts on a chip is discussed This is a hierarchical top-down approach that is useful for both of the above designs A two-dimensional detailed routing problem and the rip-up and rerouting problem are also discussed The field of computational geometry and its application to layout-in particular, to gridless routing and compaction-are reviewed, and layout engines are considered >

Recent advances in VLSI layout

Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them.
Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ different methods such as series expan- sion, linear programming, linear matrix inequalities, collocation methods, al- gebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function.

https://www.aimsciences.org/article/exportPdf?id=ee7e4111-9a13-4e44-95c8-14c5557278fc

Review on computational methods for Lyapunov functions

Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arrangement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferably extend in three directions that are angularly displaced from each other by 60°. The conductors that extend in the three directions are preferably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed. A novel device called a "tri-ister" is disclosed. Triangular devices are disclosed, including triangular NAND gates, triangular AND gates, and triangular OR gates. A triangular op amp and triode are disclosed. A triangular sense amplifier is disclosed. A DRAM memory array and an SRAM memory array, based upon triangular or parallelogram shaped cells, are disclosed, including a method of interconnecting such arrays. A programmable variable drive transistor is disclosed. CAD algorithms and methods are disclosed for designing and making semiconductor devices, which are particularly applicable to the disclosed architecture and tri-directional three metal layer routing.

CAD for hexagonal architecture

Let one face of a cube be dissected into rectangles, no 4 of which meet at a single point The dual graph of this configuration is a 4-connected triangulated plane graph This paper shows that any 4-connected plane triangulation with at least 6 vertices and at least one vertex of degree 4 is dual to a cube with one face dissected into rectangles The proof of this result contains an implicit algorithm for obtaining such a dissection The paper also discusses a related problem: Given a graph G with all faces triangular except the outer face, does there exist a dissection of a rectangle into rectangles for which G describes the adjacency relations among the rectangles?

Rectangular duals of planar graphs

An O(n /sup 2/) algorithm for finding a rectangular dual of a planar triangulated graph is presented. In practice, almost linear running times have been observed. The algorithm is useful for solving area planning problems in VLSI IC design.

An Algorithm for Finding a Rectangular Dual of a Planar Graph for Use in Area Planning for VLSI Integrated Circuits

Three types of system equivalent relations are introduced to unify existing definitions of system equivalence. Called α-, β- and γ-equivalence, their characteristics are examined mathematically and physically. Based on those definitions, two phase-variable canonical forma are developed for linear, multi-input, multi-output systems, resulting in a canonical form for control and a canonical form for observation. It is shown that a characteristic quantity called a stage sequence can be defined for a given system to uniquely determine its equivalent system in the canonical forms. The compact structures of these canonical forms are convenient representations of the mathematical and physical compositions of systems and for subsequent system analyses.

Phase-variable canonical forms for linear, multi-input, multi-output systems†

A new methodology is presented for the solution of the multilayer routing problem that has the potential to outperform channel based multi-layer routing algorithms by expanding the routing regions to include areas over the cells. It is assumed that four routing layers are available. Routing is completed in two steps; a selected group of nets is routed in the between-cell areas using existing channel routing algorithms and the first two routing layers. Then the remaining nets are routed over the entire layout area, between-cell and over-cell areas, using a new two-dimensional router and the next two routing layers. The router used for over-cell routing recognizes arbitrarily sized obstacles, for example, due to power and ground routing or sensitive circuits in the underlying cells. The proposed router was tested on a number of macro-cell layout examples. Advantages of dedicating two routing layers for over-cell routing is illustrated. Results show a significant reduction in total layout area, wire length and number of via when compared to results obtained using two-layer or multi-layer channel routing methods.

Edwin Kinnen

Papers

Rectangular duals of planar graphs

An Algorithm for Finding a Rectangular Dual of a Planar Graph for Use in Area Planning for VLSI Integrated Circuits

Phase-variable canonical forms for linear, multi-input, multi-output systems†

A multi-layer router utilizing over-cell areas

The Application of Electrical Impedance Plethysmography to the Study of Gingival Circulation