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This paper discusses the hidden-surface problem from tile point of view of sorting. The various surfaces of an object to be shown in hidden-surface or hidden-line form must be sorted to find out which ones are visible at various places on the screen. Surfaces may be sorted by lateral position in the picture (X I'), by depth (Z), or by other criteria. The paper shows that the order of sorting and the types of sorting used form differences among the existing hidden-surface algorithms. To reduce the work of sorting, each algorithm capitalizes on some coherence property of the objects represented. ‘Scan-line coherence,’ the fact that one TV scan line of output is likely to be nearly the same as the previous TV scan line, is one commonly used kind of coherence. ‘Frame coherence,’ the fact that the entire picture does not change very much between successive frames of a motion picture can be very helpful if it is applicable. By systematically looking for additional kinds of coherence and untried sorting orders and sorting types, the paper is able to suggest two promising new approaches to the hidden-surface problem. The first, a combination of three existing algorithms, is promising because it would capitalize on both frame and scan-line coherence. The second new approach would sort in the order Y, Z, X, … the only sorting order for which an existing algorithm could not be found. [ABSTRACT FROM AUTHOR]

A sparse matrix is defined to be a matrix containing a high proportion of elements that are zeros. Sparse matrices of large order are of great interest and application in science and industry; for example, electrical networks, structural engineering, power distribution, reactor diffusion, and solutions to differential equations. While conclusions within this paper are primarily drawn considering orders of greater than 1000, much is applicable to sparse matrices of smaller orders in the hundreds. Because of increasing use of large order sparse matrices and the tendency to attempt to solve larger order problems, great attention must be focused on core storage and execution time. Every effort should be made to optimize both computer memory allocation and execution times, as these are the limiting factors that most often dictate the practicality of solving a given problem. Indexing algorithms are the subject of this paper, as they are generally recognized as the most important factor in fast and efficient processing of large order sparse matrices. Indexing schemes of main interest are the bit map, address map, row-column, and the threaded list. Major variations of the indexing techniques above mentioned are noted, as well as the particular indexing scheme inherent in diagonal or band matrices. The concluding section of the paper compares the types of methods, discusses their suitability for different types of processing, and makes suggestions concerning the adaptability and flexibility of the major existing methods of indexing algorithms for application to user problems. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm for a ship scheduling problem, obtained from a Swedish ship-owning company. The algorithm uses the Dantzig-Wolfe decomposition method for linear programming. The subprograms are simple network flow problems that are solved by dynamic programming. The master program in the decomposition algorithm is an LP problem with only zero-one elements in the matrix and the right-hand side. Integer solutions are not guaranteed, but generation and solution of a large number of problems indicates that the frequency of fractional solutions is as small as 1-2 per cent. Problems with about 40 ships and 50 cargoes are solved in about 2.5 minutes on an IBM 7090. In order to resolve the fractional cases, some integer programming experiments have been made. The results will be reported in a forthcoming paper. [ABSTRACT FROM AUTHOR]

The article presents a list of papers published in the 1973 issue of the periodical. Some papers are "Announcements," "API Method Extended," "Airline Crew-Scheduling," "Air-Cargo Deployment Combat Personnel," "Aircraft Average Number Collisions," "Collision Probabilities," "Large Relative Velocity," "Special Cases, Velocity," "Air Fleet Evaluation Model (AFEM)," "Airports, Parallel Runways," "Air Routes, Potential Conflict," "Air-Route Network Planning," "Augmented Predecessor Indexing Method," "Books of Interest," "Brisbane City Council Transport Services, Note," "Broken Shifts, Bus Scheduling," "Bus Crew Scheduling," "Chesapeake Bay Bridge Traffic Control," "Column Generation Algorithm," "Combat Personnel, Equipment, Deployment," "Comparison, Steady-State and Simulation Methods," "Designing Transportation Networks," "Digital Simulation, Freeway Traffic, Long Island Expressway, New York," "Facility Location Algorithm," "Feeder Transit Lines," "Freeway Traffic, Digital Simulation," "General Networks Lemmas," "Generalized Network Problems," and "Generalized Transportation Problems."

This paper describes various forms of line drawing representation, compares different schemes of quantization, and reviews the manner in which a line drawing can be extracted from a tracing or a photographic image. The subjective aspects of a line drawing are examined. Different encoding schemes are compared, with emphasis on the so-called chain code which is convenient for highly irregular line drawings. The properties of chain-coded line drawings are derived, and algorithms are developed for analyzing line drawings to determine various geometric features. Procedures are described for rotating, expanding, and smoothing line structures, and for establishing the degree of similarity between two contours by a correlation technique. Three applications are described in detail: automatic assembly of jigsaw puzzles, map matching, and optimum two-dimensional template layout. [ABSTRACT FROM AUTHOR]

This paper describes the evolution of language features for multiprogramming from event queues and semaphores to critical regions and monitors. It suggests that the choice of language concepts should be guided by two simple principles: First, it should be possible to understand a concurrent program in time- independent terms by an effort proportional to its size; secondly, it should be possible to state assumptions about invariant relationships among program components and have these assumptions checked automatically. The central problems of multiprogramming are illustrated by annotated algorithms written in a well-structured programming language. [ABSTRACT FROM AUTHOR]

The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented. [ABSTRACT FROM AUTHOR]

In many transit systems, vehicles depart their originating stops at fixed intervals, but headways become increasingly irregular as they move along the line. This paper considers how best to control such randomness through a strategy based on holding individual vehicles at a chosen control stop. An algorithm is presented for constructing an approximate optimal dispatching strategy from the control point, where optimal is defined both in terms of average passenger wait at the control stop and average delay for riders already aboard the vehicle. The algorithm is used on actual operations data from a Boston subway line to propose service improvements. [ABSTRACT FROM AUTHOR]

This paper presents a method for serial combination of truck trips to minimize the total cost of deadheading, subject to constraints on the allowed combinations. The problem is initially formulated as an integer transportation problem with extra compatibility constraints, and then reduced to a classical transportation problem. Modifications of the classical algorithm led to a fifty-fold reduction in computer time, and permit solution of a 1000 × 1000 problem in less than two minutes of computer time. Implementation of the method led to considerable cost savings over the older manual procedure. [ABSTRACT FROM AUTHOR]

This paper is addressed to the problem of locating the absolute and vertex centers (minimax criterion) of an undirected tree graph. Based upon a convexity property of the criterion function a very simple and efficient algorithm is offered that locates the minimax point by locating first a maximax point. The minimax is at the mid-point of the maximum path from the maximax point. The vertex center is located simultaneously. [ABSTRACT FROM AUTHOR]

An inductive inference problem will often be structured so that the target variable (hypotheses) are logically distant from the observable events (data). In this situation it may be difficult or impossible to assess the probabilistic connection between them, but it may be possible to decompose the problem through the use of intermediate or explanatory variables. That is, it will often be possible to assess the likelihood of the observed data given some intermediate variable, and the likelihood of that intermediate variable given another, and so on, until the hypotheses of interest are reached. Inferences which incorporate one or more intermediate variables are called hierarchical, cascaded, or multistage inferences. The present paper presents a normative model for the solution of the general hierarchical inference problem. The formulation begins with a formal description of the hierarchical inference tree, including a discussion of various simplifying conditional independence assumptions. The solution is first derived for three special case models of differing structure, and then the algorithm for the general solution is given for two cases: one in which the conditional independence assumptions have been made and one in which they have not. [ABSTRACT FROM AUTHOR]

The bibliography appearing at the end of this article lists 37 sorting algorithms and 100 books and papers on sorting published in the last 20 years. The basic ideas presented here have been abstracted from this body of work, and the best algorithms known are given as examples. As the algorithms are explained, references to related algorithms and mathematical or experimental analyses are given. Suggestions are then made for choosing the algorithm best suited to a given situation. [ABSTRACT FROM AUTHOR]

In this paper it is assumed that, using a sample survey, two factors are to be studied, comparisons between the "levels" of the factors are of greatest interest, and there is "interaction" between the factors. Attention is concentrated on situations in which only two levels of each factor are to be compared, but extensions to more complex surveys are discussed. Assuming independent sampling, optimal sample size allocations are obtained. Where these allocations require recourse to programming algorithms, approximate solutions are given. If independent sampling is not feasible, a double sampling procedure is suggested. To indicate how sub-sampling from the first phase sample is to be carried out, a sampling rule (possessing optimal conditional precision properties) is derived. Then, a procedure to determine the optimal first phase sample size is given. Finally, it is demonstrated that this double sampling procedure can be applied to estimation of the (finite) population mean when double sampling with stratification is used. [ABSTRACT FROM AUTHOR]

The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable costs, associated with sampling in the ith stratum. The resulting algorithm is noted to be applicable in finding the optimal allocation of sampling effort (with fixed and variable sampling costs) under a variety of distributional assumptions. An interpretation is also given to two and higher stage design questions when there is differential prior information regarding the first stage units. [ABSTRACT FROM AUTHOR]

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the procedure and a few areas of application are indicated. [ABSTRACT FROM AUTHOR]

The general problem is that of locating a central facility in a network so as to minimize the sum of its distances from the sources of flow to it, each distance being appropriately weighted to reflect the associated flow volume and/or cost. In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle. The first algorithm is based on a reduction procedure that may also yield useful simplification of problems involving general networks. [ABSTRACT FROM AUTHOR]

This paper presents a method for developing efficient timetables for the operation of fixed schedule common-carrier passenger transportation systems. The ability to compute such timetables is needed in the consideration of planning alternatives for future transportation systems and/or the efficient operation of existing systems. Here, time- table optimization is accomplished by maximizing an objective function consisting of three basic components: operating costs, revenues, and traveler benefits. Traveler benefits are computed using a consumer preference model that specifies a traveler's willingness to pay for alternative trips, based on the scheduling of those trips. The optimization is based on successive iterations of a dynamic programming algorithm that develops timetables for each vehicle in the system. Solutions are termed optimal to within a 'first-order passenger exchange! Examples are presented to illustrate the utilization of the methodology for computing information relevant to the development of system operating policies and to the consideration of planning alternatives. [ABSTRACT FROM AUTHOR]

This paper develops a dynamic programming model for selecting an optimal combination of transportation modes over a multiperiod planning horizon. The formulation explicitly incorporates uncertainty regarding future requirements or demands for a number of commodity classes. In addition to determining the optimal modes to employ, the model assigns individual commodity classes to various modes, determines which supply points serve which destinations, and reroutes carriers from destinations to alternative sources where they will be most effective. The model is formulated as an optimal discrete time stochastic control problem where cost is quadratic and dynamic equations linear in the state and control variables. This model may be solved in closed form by an efficient dynamic programming algorithm that permits the treatment of relatively large scale systems. A iso developed is an alternative, generally suboptimal method of solution, based upon wiving a sequence of convex programming problems over time. This technique may be employed for a more general class of problems. In both methods the use of 'shadow prices' that arise is discussed. [ABSTRACT FROM AUTHOR]

In this paper the authors find the optimal allocation of servicing periods to a facility servicing N incoming traffic streams. In our model it is assumed that stream flows are deterministic, that there is a fixed amount of lime lost, τi , when the server switches attention from the ith to the i + 1st stream and that the objective is to minimize time average delay. [ABSTRACT FROM AUTHOR]

In many cases Bayes' theorem is an appropriate algorithm for the aggregation of probabilistic evidence. As with other statistical procedures, there are restrictions that must be taken into account. In the present paper we shall comment on several approaches that have been devoted to one of these restrictions; the incorporation of uncertainty about the true state of a datum. A datum is a variable which can be partitioned into equivalence classes. These classes represent the possible data states which will be also called events. In Bayes' theorem an event is an item of information which will be used for revising the opinion about the relative likelihood of hypotheses. In any specific situation only one of the possible events will be the true event. An event may come from a source whose reporting or observational accuracy is not perfect. An example may illustrate the issue. A medical doctor wants to come to a diagnosis. To achieve this he considers several data. One datum might be the result of a medical test, which has three possible states: positive, negative, inconclusive. If the doctor reports the state of the datum to be positive, he may be wrong by whatever reasons. That is, the report of an event must not necessarily coincide with the actual or true event of the datum under consideration. This kind of uncertainty about the true event in any specific situation is a characteristic of the source. In most cases it will reduce the diagnostic impact of an event. Whenever the report of an event and the true event coincide imperfectly, measures of source inaccuracy must be incorporated into Bayes' theorem. The task can be considered as two stage probabilistic induction. The first step is induction from the reported to the actual event, the second is induction from the actual event to the creditation of hypotheses. This is the reason why Gettys and Willke (1969) speak about "cascaded inference." [ABSTRACT FROM AUTHOR]

This paper discusses the application of Bayes's theorem to those cases where the true state of the world is not known with certainty. An algorithm is proposed that relaxes the requirement of Bayes's theorem that the true data state be known with certainty by postulating a true but unobservable elementary event, ω, which gives rise to posterior probabilities which reflect the uncertainty of the data. A derivation is presented for the calculation of Bayesian posterior probabilities which uses as its input these probabilities, rather than the true event, o, which is assumed to be unavailable. Suggestions are made as to the application of this modification of Bayes's theorem to cascaded inference processes. [ABSTRACT FROM AUTHOR]

Queueing models of time-sharing algorithms have been appearing in the literature with increasing frequency. This survey delineates the parameters which distinguish the different analytic models and presents the research results of most of the papers to date. The techniques used in analyzing various round-robin models and multiple-level queue models both with and without priorities are emphasized. The results indicated provide the system designer with a number of degrees of freedom with which to synthesize a time-shared processing system and point out needed research directions. An annotated bibliography is provided. [ABSTRACT FROM AUTHOR]

The article comments on the applicability of the set theory in sociological research. The author notes that Donal E. Muir's paper "Searching Data for Predictive Variables: A Set-Theoretical Approach" contributes to the improved scientific status of sociology specifically by investigating one of its most ubiquitous and problematic predicates. In doing this, Muir displays the utility of set theory as a primitive but formidable tool for the construction of sociological sentences. The author further points out that set theory is a rich and sophisticated language, with an array of conjunctions with which to build complicated subject and object sets. Above all, it offers a variety of unambiguous predicates with which to build logically meaningful theory, that is, theory that has implications, which can be proven to be true by the rules of deductive logic. The article further reveals that Muir has attacked the basic scientific predicate, cause, and has come up with a useful if not revolutionary algorithm. He has moved toward the improvement of sociological sentence structure.