A bucketing algorithm for the orthogonal segment intersection search problem and its practical efficiency

The orthogonal segment intersection search problem is stated as follows: given a setS ofn orthogonal segments in the plane, report all the segments ofS that intersect a given orthogonal query segment. For this problem, we propose a simple and practical algorithm based on bucketing techniques. It constructs, inO(n) time preprocessing, a search structure of sizeO(n) so that all the segments ofS intersecting a query segment can be reported inO(k) time in the average case, wherek is the number of the reported segments. The proposed algorithm as well as existing algorithms is implemented in FORTRAN, and their practical efficiencies are investigated through computational experiments. It is shown that ourO(k) search time,O(n) space, andO(n) preprocessing time algorithm is in practice the most efficient among the algorithms tested.Supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture of Japan under Grant No. 62550270 (1987).     

A bucketing algorithm for the orthogonal segment intersection search problem and its practical efficiency

The orthogonal segment intersection search problem is stated as follows: given a setS ofn orthogonal segments in the plane, report all the segments ofS that intersect a given orthogonal query segment. For this problem, we propose a simple and practical algorithm based on bucketing techniques. It constructs, inO(n) time preprocessing, a search structure of sizeO(n) so that all the segments ofS intersecting a query segment can be reported inO(k) time in the average case, wherek is the number of the reported segments. The proposed algorithm as well as existing algorithms is implemented in FORTRAN, and their practical efficiencies are investigated through computational experiments. It is shown that ourO(k) search time,O(n) space, andO(n) preprocessing time algorithm is in practice the most efficient among the algorithms tested.     

A parallel intersection algorithm for vector polygon overlay

A parallel intersection algorithm for speeding the creation of a composite network of polygons whose identities relate to the original polygons from which they are formed in vector geographic information systems (ISs) is described. The algorithm reduces unnecessary intersection checking, especially when polygon density is high. Single-stream and multiple-stream versions of the algorithm are discussed. Experimental results illustrating the overall performance of the parallel algorithm are presented     

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

An algorithm for line intersection identification

An algorithm for identifying line intersection is presented.⁽¹⁾ The algorithm has been implemented on a microprocessor system for evaluation of the complexity of nerve structures. Data is entered by use of a sonic pen digitizing tablet. The tablet permits tracing a projected image and entering the positional data into the microprocessor program.     

A hybrid direction algorithm for solving linear programs

In this paper we suggest a new ascent direction for the adaptive method developed by Gabasov et al. (A method of solving general linear programming problems, Doklady AN BSSR 23(3) (1979), pp. 197–200 (in Russian)) for solving linear programs with bounded variables. A quantity called optimality estimate is defined, necessary and sufficient conditions of optimality based on this estimate are derived. An algorithm called the adaptive method with hybrid direction (AMHD) is suggested and a numerical example is given for illustration purpose. In order to compare the suggested algorithm with the classical primal simplex algorithm employing Dantzig's rule (PSA), we have developed a numerical implementation under the MATLAB programming language. The experimental study involves the CPU time and the iterations number of the two algorithms applied to solve randomly generated test problems of different dimensions. It has been shown that when the problem dimension increases, the superiority of AMHD over primal simplex algorithm increases.     

A fast robust algorithm for the intersection of triangulated surfaces

The use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform Boolean operations between groups of triangulated surfaces. In the intersection process, an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections. An algorithm based on tracing the neighbours of intersecting triangles (TNOIT) is proposed to determine the intersection lines. Given the node numbers at the vertices of the triangles, the neighbour relationship is first established. A background grid is employed to limit the scope of searching for candidate triangles that may intersect. This will drastically reduce the time of geometrical checking for intersections between triangles, making the surface intersection and mesh generation a quasi-linear process with respect to the number of elements involved. In the determination of intersection between two triangles, four fundamental cases are identified and treated systematically to enhance robustness and reliability. Tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process, it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned. Five examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm.     

A robust algorithm for random parameter tracking

An algorithm for tracking time-varying parameters is studied. It is shown to be exponentially stable independently of the choice of algorithm parameters. We derive some useful nonasymptotic estimates for the tracking error and develop the asymptotically optimal version of the method     

A new algorithm for an eigenvalue assignment problem from singularcontrol theory

In this paper, a new numerical algorithm for an eigenvalue assignment problem, which arises from a singular system control, is developed. The algorithm is based on orthogonal row/column compressions which can be implemented in a numerically reliable way     

A branch-and-price algorithm for an integrated production and inventory routing problem

With globalization, the need to better integrate production and distribution decisions has become ever more pressing for manufacturers trying to streamline their supply chain. This paper investigates a previously developed mixed-integer programming (MIP) model aimed at minimizing production, inventory, and delivery costs across the various stages of the system. The problem being modeled includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of homogeneous vehicles. Demand can be satisfied from either inventory held at a customer site or from daily product distribution. Whether a customer is visited on a particular day is determined by an implicit tradeoff between inventory and distribution costs. Once the decision is made, a vehicle routing problem must be solved for those customers who are scheduled for a delivery.A hybrid methodology that combines exact and heuristic procedures within a branch-and-price framework is developed to solve the underlying MIP. The approach takes advantage of the efficiency of heuristics and the precision of branch and price. Implementation required devising a new branching strategy to accommodate the unique degeneracy characteristics of the master problem, and a new procedure for handling symmetry. A novel column generation heuristic and a rounding heuristic were also implemented to improve algorithmic efficiency. Computational testing on standard data sets showed that the hybrid scheme can solve instances with up to 50 customers and 8 time periods within 1 h. This level of performance could not be matched by either CPLEX or standard branch and price alone.     

A feasible direction algorithm for general nonlinear semidefinite programming

This paper deals with nonlinear smooth optimization problems with equality and inequality constraints, as well as semidefinite constraints on nonlinear symmetric matrix-valued functions. A new semidefinite programming algorithm that takes advantage of the structure of the matrix constraints is presented. This one is relevant in applications where the matrices have a favorable structure, as in the case when finite element models are employed. FDIPA_GSDP is then obtained by integration of this new method with the well known Feasible Direction Interior Point Algorithm for nonlinear smooth optimization, FDIPA. FDIPA_GSDP makes iterations in the primal and dual variables to solve the first order optimality conditions. Given an initial feasible point with respect to the inequality constraints, FDIPA_GSDP generates a feasible descent sequence, converging to a local solution of the problem. At each iteration a feasible descent direction is computed by merely solving two linear systems with the same matrix. A line search along this direction looks for a new feasible point with a lower objective. Global convergence to stationary points is proved. Some structural optimization test problems were solved very efficiently, without need of parameters tuning.     

A simulation-based heuristic algorithm for disposition of direction finders

A direction finder is a military weapon that is used to find locations of targets that emit radio frequencies. Multiple direction finders are used in a direction finder system for finding locations of targets in an area of interest. We present a two-stage heuristic algorithm for disposing direction finders in a direction finder system for the objective of maximizing the accuracy of estimation of the location of a target that is assumed to be located in the area of interest. In the suggested heuristic algorithm, a simulation-based method is used for estimating the probability of coverage, the probability that a target is in a given region (of a given size) surrounding the estimated location of the target, and another simulation-based method and a local search method are used to determine locations of direction finders that result in the maximum probability of coverage. Performance of the suggested algorithm is evaluated through computational experiments and results show that the algorithm gives a good disposition plan in a reasonable amount of computation time.     

A random least-trimmed-squares identification algorithm

The Least-trimmed-squares (LTS) estimator is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. In this paper, we propose a random LTS algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval. Moreover, if the number of data points goes to infinite, the algorithm becomes a deterministic one that converges to the true LTS in some probability sense.     

Analysis and parameter selection for an adaptive random search algorithm

This paper presents an analysis of an adaptive random search (ARS) algorithm, a global minimization method. A probability model is introduced to characterize the statistical properties of the number of iterations required to find an acceptable solution. Moreover, based on this probability model, a new stopping criterion is introduced to predict the maximum number of iterations required to find an acceptable solution with a pre-specified level of confidence. Finally, this paper presents a systematic procedure for choosing the user-specified parameters in the ARS algorithm for fastest convergence. The results, which are valid for search spaces of arbitrary dimensions, are illustrated on a simple three-dimensional example.     

The language intersection problem for non-recursive context-free grammars

We prove that, given as input two context-free grammars, deciding non-emptiness of intersection of the two generated languages is PSPACE-complete if at least one grammar is non-recursive. The problem remains PSPACE-complete when both grammars are non-recursive and deterministic. Also investigated are generalizations of the problem to several context-free grammars, of which a certain number are non-recursive.     

A highly optimized algorithm for continuous intersection join queries over moving objects

Given two sets of moving objects with nonzero extents, the continuous intersection join query reports every pair of intersecting objects, one from each of the two moving object sets, for every timestamp. This type of queries is important for a number of applications, e.g., in the multi-billion dollar computer game industry, massively multiplayer online games like World of Warcraft need to monitor the intersection among players’ attack ranges and render players’ interaction in real time. The computational cost of a straightforward algorithm or an algorithm adapted from another query type is prohibitive, and answering the query in real time poses a great challenge. Those algorithms compute the query answer for either too long or too short a time interval, which results in either a very large computation cost per answer update or too frequent answer updates, respectively. This observation motivates us to optimize the query processing in the time dimension. In this study, we achieve this optimization by introducing the new concept of time-constrained (TC) processing. Further, TC processing enables a set of effective improvement techniques on traditional intersection join algorithms. Finally, we provide a method to find the optimal value for an important parameter required in our technique, the maximum update interval. As a result, we achieve a highly optimized algorithm for processing continuous intersection join queries on moving objects. With a thorough experimental study, we show that our algorithm outperforms the best adapted existing solution by several orders of magnitude. We also validate the accuracy of our cost model and its effectiveness in optimizing the performance.