Research and Advances

The selection of optimal tab settings

A new generation of computer terminals allows tab settings to be selected and set by the computer. This feature can be used to reduce the number of characters that are needed to represent a document for transmission and printing. In this note, an algorithm is given for selecting the optimal set of tab stops for minimizing the number of characters transmitted. An implementation of the algorithm has reduced the number of characters transmitted by from 7 to 30 percent, but requires a prepass through the document to compute a matrix used in determining the optimal set of tab stops. The use of fixed tab stops, as a heuristic alternative, can achieve about 80 percent of optimal with no prepass.


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Research and Advances

Efficient generation of the binary reflected gray code and its applications

Algorithms are presented to generate the n-bit binary reflected Gray code and codewords of fixed weight in that code. Both algorithms are efficient in that the time required to generate the next element from the current one is constant. Applications to the generation of the combinations of n things taken k at a time, the compositions of integers, and the permutations of a multiset are discussed.
Research and Advances

Backtrack programming techniques

The purpose of this paper is twofold. First, a brief exposition of the general backtrack technique and its history is given. Second, it is shown how the use of macros can considerably shorten the computation time in many cases. In particular, this technique has allowed the solution of two previously open combinatorial problems, the computation of new terms in a well-known series, and the substantial reduction in computation time for the solution to another combinatorial problem.

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