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.Storing computed cell masses is introduced as a method for reducing the amount of calculation for each iteration of the algorithm. Adding the distance from the goal to the path cost function, and expanding the most recently encountered cell, are shown to substantially reduce the number of iterations needed. Index Terms-Cell coding, heuristic search, Lee algorithm, path cost function, printed circuit board, rectangular grids, shortest path problem, wire routing.
A search procedure is given which will determine whether Hamilton paths or circuits exist in a given graph, and will find one or all of them. A combined procedure is given for both directed and undirected graphs. The search consists of creating partial paths and making deductions which determine whether each partial path is a section of any Hamilton path whatever, and which direct the extension of the partial paths.
A system for the compression of data files, viewed as strings of characters, is presented. The method is general, and applies equally well to English, to PL/I, or to digital data. The system consists of an encoder, an analysis program, and a decoder. Two algorithms for encoding a string differ slightly from earlier proposals. The analysis program attempts to find an optimal set of codes for representing substrings of the file. Four new algorithms for this operation are described and compared. Various parameters in the algorithms are optimized to obtain a high degree of compression for sample texts.
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