April 1979 - Vol. 22 No. 4

An algorithm for detecting occurrences of a three-dimensional pattern of objects within a larger structure is presented. The search technique presented uses the geometric structure of the pattern to define characteristics demanded of candidates for matching. This is useful in cases where the properties of each atom, considered individually, do not adequately limit the number of sets of possible matchings. Several applications of this technique in the field of chemistry are: (1) in pharmacology: searching for a common constellation of atoms in molecules possessing similar biological activities; (2) in X-ray crystallography: fitting a structure or a structural fragment to a set of peaks in the electron-density distribution of a Fourier map; (3) in chemical documentation: retrieving from a file the structures containing specified substructures.

Econometric models of the U.S. computer market have been developed to study the relationships between system price and hardware performance. Single measures of price/performance such as “Grosch's Law” are shown to be so oversimplified as to be meaningless. Multiple-regression models predicting system cost as a function of several hardware characteristics do, however, reveal a market dichotomy. On one hand there exists a stable, price predictable market for larger, general purpose computer systems. The other market is the developing one for small business computer systems, a market which is relatively unstable with low price predictability.

A macro model of a distributed information system in presented. The model describes the major costs of using an information system from the perspective of the end-user. The model is intended to provide guidance to the system designer by making evident the effect of various design and operating parameters on overall cost per transaction. The technique is illustrated by application to the design of an interactive transaction processing system.

An efficient and numerically stable method is presented for the problem of updating an orthogonal decomposition of a matrix of column (or row) vectors. The fundamental idea is to add a column (or row) analogous to adding an additional row of data in a linear least squares problem. A column (or row) is dropped by a formal scaling with the imaginary unit, √-1, followed by least squares addition of the column (or row). The elimination process for the procedure is successive application of the Givens transformation in modified (more efficient) form. These ideas are illustrated with an implementation of the revised simplex method. The algorithm is a general purpose one that does not account for any particular structure or sparsity in the equations. Some suggested computational tests for determining signs of various controlling parameters in the revised simplex algorithm are mentioned. A simple means of constructing test cases and some sample computing times are presented.

This paper describes efficient new heuristic methods to color the vertices of a graph which rely upon the comparison of the degrees and structure of a graph. A method is developed which is exact for bipartite graphs and is an important part of heuristic procedures to find maximal cliques in general graphs. Finally an exact method is given which performs better than the Randall-Brown algorithm and is able to color larger graphs, and the new heuristic methods, the classical methods, and the exact method are compared.