Masao Iri

An algorithm for diagnosis of system failures in the chemical process

Abstract An attempt was made to apply graph theory to the diagnosis of the system failures in the chemical process. A signed digraph is used for a mathematical model representing the influences among elements of the system. The concept of a pattern on the signed digraph is introduced for representing a state of the system. In order to eliminate carrying out the complicated and inefficient quantitative simulation, the mathematical model of the system structure to represent the rpopagation of failures is simplified in a qualitative fashion. The origin of the system failure can be located at the maximal strongly-connected component in the cause-effect graph reflecting the pattern of abnormality. Even when the pattern is observed only partially, the assumption of single origin of the failure reduces, to some extent, the range of possible candidates to be the first cause of the failure.

Computational-geometric methods for polygonal approximations of a curve

In cartography, computer graphics, pattern recognition, etc., we often encounter the problem of approximating a given finer piecewise linear curve by another coarser piecewise linear curve consisting of fewer line segments. In connection with this problem, a number of papers have been published, but it seems that the problem itself has not been well modelled from the standpoint of specific applications, nor has a nice algorithm, nice from the computational-geometric viewpoint, been proposed. In the present paper, we first consider (i) the problem of approximating a piecewise linear curve by another whose vertices are a subset of the vertices of the former, and show that an optimum solution of this problem can be found in a polynomial time. We also mention recent results on related problems by several researchers including the authors themselves. We then pose (ii) a problem of covering a sequence of n points by a minimum number of rectangles with a given width, and present an O(n long n )-time algorithm by making use of some fundamental established techniques in computational geometry. Furthermore, an O(mn (log n ) 2 )-time algorithm is presented for finding the minimum width w such that a sequence of n points can be covered by at most m rectangles with width w . Finally, (iii) several related problems are discussed.

Polygonal Approximations of a Curve — Formulations and Algorithms

Abstract A general framework for polygonal approximation problems in various situations is given, and solution algorithms are discussed. The problems are classified according to three criteria: (1) whether the curve is the graph of a piecewise linear function y=f(x) of the independent variable x, or it is a general polygonal curve in the plane, (2) which error criterion is adopted (for a piecewise linear function, we consider only one criterion), (3) whether the objective is to minimize the number of vertices of the approximate curve when an error bound is given, or to minimize the approximation error when the number of vertices of the approximate curve is specified. The problems are first formulated in terms of graph theory, and then computationally efficient algorithms are constructed by taking advantage of fundamental algorithms for convex hulls in computational geometry.

Construction of the Voronoi diagram for 'one million' generators in single-precision arithmetic

A numerically stable algorithm for constructing Voronoi diagrams in the plane is presented. In this algorithm higher priority is placed on the topological structure than on numerical values, so that, however large the numerical errors, the algorithm will never come across topological inconsistency and thus can always complete its task. The behavior of the algorithm is shown with examples, including one for as many as 10/sup 6/ generators. >

Voronoi Diagram in the Laguerre Geometry and Its Applications

We extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line, and show that there is an

An improved algorithm for diagnosis of system failures in the chemical process

O(n\log n)

A multiplicative barrier function method for linear programming

algorithm for this extended case. The Voronoi diagram in the Laguerre geometry may be applied to solving effectively a number of geometrical problems such as those of determining whether or not a point belongs to the union of n circles, of finding the connected components of n circles, and of finding the contour of the union of n circles. As in the case with ordinary Voronoi diagrams, the algorithms proposed here for those problems are optimal to within a constant factor. Some extensions of the problem and the algorithm from different viewpoints are also suggested.

Simultaneous Computation of Functions, Partial Derivatives and Estimates of Rounding Errors : Complexity and Practicality

Abstract The detailed techniques for improving the efficiency of a fault-diagnosis algorithm can be based on the signed directed graph. This graph represents the structure of the system, and the pattern on the graph represents a state of the system. The usefulness of the improved algorithm is demonstrated using a model of a chemical process comprising a reactor, a heat exchanger and a distillation tower.

Practical use of Bucketing Techniques in Computational Geometry

A simple Newton-like descent algorithm for linear programming is proposed together with results of preliminary computational experiments on small- and medium-size problems. The proposed algorithm gives local superlinear convergence to the optimum and, experimentally, shows global linear convergence. It is similar to Karmarkars algorithm in that it is an interior feasible direction method and self-correcting, while it is quite different from Karmarkars in that it gives superlinear convergence and that no artificial extra constraint is introduced nor is protective geometry needed, but only affine geometry suffices.

Use of matroid theory in operations research, circuits and systems theory

A practical approach is proposed to the problem of simultaneously computing a function, its partial derivatives with respect to all the variables, and an estimate of the rounding error incurred in the computed value of the function. Theoretically, it has a complexity at most a constant times as large as that of evaluating the function alone, the constant being independent of the number of variables of the function, and it is an alternative graphical interpretation of W. Baur and V. Strassen’s results, with some generalizations. Practically, it is stated in a form easily implementable as a computer program, which enables us to automatically compute the derivatives if we are given only the program for computing the function. Remarks are added also on the cases of several functions, of higher derivatives and of non-straght-line programs, and on application to problems containing differential equations.