Lee's Algorithm Research Articles

An automatic cell pattern generation system for CMOS transistor-pair array LSI

In an automatic layout design system for masterslice or gate array LSI, a cell library must be provided in advance. Manual preparation of such a cell library requires a considerable amount of design effort and turnaround time. In this paper, an automatic cell pattern generation algorithm and its program implementation for a CMOS transistor-pair array masterslice are presented. The cell pattern generation process consists of the transistor-pair extraction, transistor-pair placement and routing phases. The transistor-pair placement method is based on an iterative improvement algorithm for wiring congestion. For the wiring phase, Lee's maze routing algorithm is modified for application to polysilicon, diffusion and two aluminum layers. Furthermore, a new interconnection ordering algorithm is proposed and its effectiveness for attaining higher wireability is experimentally shown. Finally, it is shown that the proposed cell pattern generation system achieves a significant reduction of cell pattern design time compared to conventional manual design.

Adaptive Noise Smoothing Filter for Images with Signal-Dependent Noise

In this paper, we consider the restoration of images with signal-dependent noise. The filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean, nonstationary variance (NMNV) image model. For images degraded by a class of uncorrelated, signal-dependent noise without blur, the adaptive noise smoothing filter becomes a point processor and is similar to Lee's local statistics algorithm [16]. The filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal-dependent noise. For multiplicative noise, the adaptive noise smoothing filter is a systematic derivation of Lee's algorithm with some extensions that allow different estimators for the local image variance. The advantage of the derivation is its easy extension to deal with various types of signal-dependent noise. Film-grain and Poisson signal-dependent restoration problems are also considered as examples. All the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required.

ARMA Modelling using Circular Lattice Filter

A method for recursive estimation of the parameters of ARMA processes is proposed by using the circular lattice filter recently derived by the authors. This filter is originally proposed for estimating the parameters of multivariate AR processes and contains only scal ar operations. As Lee, Friedlander, and Morf have done, by regarding a scalar ARMA. process as a degenerate two variates AR process, we can apply the circular lattice algorithm to ARMA modelling. But our approach is more direct, since we deal with scalar quantities only and the benefit of this is that the number of multiplications per one sample of our algorithm is about 60% of that of Lee's algorithm.

Comments on "A Compilation Technique for Exact System Reliability" - II

The K.K. Lee algorithm incorrectly evaluates system reliability when the system model contains replicated events.

A note on lee and schachter's algorithm for delaunay triangulation

Lee and Schachter have presented an algorithm for the Delaunay triangulation of a set of points whose convex hull is a rectangular region. An addendum to that algorithm is presented which gives the Delaunay triangulation of a set of points with an arbitrary convex hull. Timing results are also given.

Experiments with routing on printed circuit boards

Several ways of utilizing Lee's wave algorithm for routing on printed circuit boards were compared. It was proved that the order of net processing influenced the quality of the solution of a given interconnection problem. Moreover, it was found that the choice of ‘source’ and ‘target’ formations influenced both the computational time and the quality of the solution. The results obtained allowed the performance of the SYSDEB77 system for routing on two-layer boards to be improved.

A probabilistic model for the analysis of the routing process for circuits

AbstractA probabilistic model is developed for studying the problem of routing printed circuits. The model, which uses the density of blockages on the carrier as a parameter, is based on the path‐searching mechanism of Lee's algorithm. Lee's algorithm is used in our analysis because it belongs to a class of pathfinding procedures which guarantee finding a path between two given points if one exists. It is shown that the routing probability, RM(d), is bounded above by PM(d), where PM(d) is the probability of existence of an arbitrary path of ideal Manhattan distance d from a given source point. Analytical computation shows that PM(d) is practically one until a density of about 35%. After this it sharply reduces, reaching a negligible value at a density of 43% for all but very small values of d. Some experiments related to the verification of the model are described. These experimental results show good agreement with the theoretically derived probabilities.

Some Variations of Lee's Algorithm

Lee's algorithm is a pathfinding algorithm, which is often used in computer-aided design systems to route wires on printed circuit boards. This paper discusses some variations of Lee's algorithm which can be used in certain contexts to improve its efficiency. First, it is shown that, by storing frontier cells in an array of stacks rather than a single list, costly searching operations can be eliminated without significantly increasing storage requirements. Second, it is shown that if each path's cost is the sum of the weights of its cells then retrace codes can be assigned to cells as soon as they are reached rather than when they are expanded. Third, it is shown that if the additional restriction is made that each cell's weight is not a function of the state of any nonneighbor cell, then an encoding scheme requiring only two bits/cell can be used for both rectangular and hexagonal grids.

Ordering the data for Lee's algorithm

It is shown that, when using Lee's algorithm for interconnection programs, if the order in which the tracks are routed is determined by the distance between the start and end points of each tracks, on average more paths may be placed than if the order is chosen at random.

The Lee Path Connection Algorithm

The Lee path connection algorithm is probably the most widely used method for finding wire paths on printed circuit boards. It is shown that the original claim of generality for the path cost function is incorrect, and a restriction, called the pathconsistency property, is introduced. The Lee algorithm holds for those path cost functions having this property. Codings for the cells of the grid are proposed which will allow the correct operation of the algorithm under the most general path cost function, using the minimum number of states possible, six states per cell. Then methods for reducing the number of calculations by increasing the number of states are presented.

Automation of etching-pattern layout

HELP (Heuristic Etching-Pattern Layout Program) is an application program developed to computerize the tedious and error-prone although vitally important wiring design of printed circuit boards. HELP helps automate a design stage one step closer to production than logical design. It can be used to design wiring patterns of two-layer circuit boards on which ICs in dual-in-line packages as well as discrete components such as transistors and resistors have been placed. HELP employs two methods of wiring. One is the heuristic method, which simulates human approaches to wiring design, and the other is the theoretically interesting but time-consuming method of maze-running, based on the Lee's algorithm. HELP performs more than 90 percent of required wiring by the heuristic method. The maze-running method finds an optimal path with respect to a performance function for each point-to-point, and point-to-line connection. It can bring the number of successful wiring connections very close to 100 percent.

Connection Routing Algorithm for Printed Circuit Boards

A generalized algorithm for forming interconnections between points on a multilayer circuit board is described and evaluated. The algorithm treats interconnections on individual layers and connections between layers by means of plated holes. Generalizing the well-known Lee algorithm and using its terminology, this algorithm makes use of a coded C array that is stored in memory and records the state of the multilayer circuit board. Completed paths, possible remaining paths between points to be connected, and circuitboard interconnection restrictions are recorded in the coded C array. The algorithm consists of five iterative steps that involve decisions on the basis of the state of the circuit board as stored in the C array. All possible routes are attempted, and the routing sequence is stopped when the path is completed or all attempted path routes are exhausted. A number of modifications to the algorithm permitting various circuit connection constraints to be satisfied are also presented. The algorithm has been programmed for a GE-635 computer. Typical results for some of the printed circuit boards that were used to evaluate the algorithm are included.

A Modification of Lee's Path Connection Algorithm

It is shown that a set of diagnostic tests designed for a redundant circuit under the single-fault assumption is not necessarily a valid test set if a fault occurrence is preceded by the occurrence of some ( undetectable) redundant faults. This is an additional reason ( besides economy) for trying to eliminate certain kinds of redundancy from the circuit. However, single-fault analysis may remain valid for some types of redundancy which serve a useful purpose, such as the elimination of logic hazards in two-level circuits.

Simplification of Lee's algorithm for special problems

Lee's algorithm (1) for solving the path problem may be simplified in special cases, as mentioned by Lee himself.