浮動小数点演算ユニットを利用した４×４行列式の適応的符号判定処理

Geometric algorithms are usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are reliable if evaluated exactly with integer arithmetic, but this degrades performance since software extended-precision arithmetic is required.

In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C(1)-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation.

Topology optimization with closed B-splines and Boolean operations

In this paper is introduced a new algorithm by index parameters at grid environment with static scheduled that this proposed algorithm is used as more efficient method than previous studied algorithms. RQSG algorithm can increase the efficiency rather than previous algorithms using index parameters, and also is introduced a new technique method using proposed algorithm for better optimizing with mixing of communication cost and fitness function. In this situation is used choosing the best tasks with RQSG algorithm to create a suitable method for solving the problem which this method didn't use in previous algorithms. It will be introduced an algorithm for optimized choosing of processing sources based on a technique method, that with this algorithm and also with various simulations is increased the reliability and dependability in competition of previous algorithms. Also this algorithm has decreased dramatically the certification time of final processing source with the most optimized state. Finally the mentioned algorithm has increased the servicing quality for using the task in processing sources and also has created the best state of optimized path in index parameters at grid environment.

We propose an efficient and exact method for the adaptive sign detection of 4×4 determinants using a standard arithmetic unit. The entities of determinants are variable length integers (integers of arbitrary bit length). The integers are expressed in 16-bit data units, and the sign detection is reduced to the computation of 4×4 determinants of 16-bit integers. To accelerate the computation, the calculation is performed by using a standard arithmetic unit. We have implemented our method and confirmed that it significantly improves the computation time of 4×4 determinants. The method can be applicable to many geometric algorithms that need the exact sign evaluation of 4×4 determinants, especially to construct robust geometric algorithms.

Diversity maximization is an important concept in information retrieval, computational geometry and operations research. Usually, it is a variant of the following problem: Given a ground set, constraints, and a function f that measures diversity of a subset, the task is to select a feasible subset S such that f(S) is maximized. The sum-dispersion function f(S) which is the sum of the pairwise distances in S, is in this context a prominent diversification measure. The corresponding diversity maximization is the or sum-sum diversification. Many recent results deal with the design of constant-factor approximation algorithms of diversification problems involving sum-dispersion function under a matroid constraint. In this paper, we present a PTAS for the max-sum diversity problem under a matroid constraint for distances d(.,.) of negative type. Distances of negative type are, for example, metric distances stemming from the l_2 and l_1 norms, as well as the cosine or spherical, or Jaccard distance which are popular similarity metrics in web and image search. Our algorithm is based on techniques developed in geometric algorithms like metric embeddings and convex optimization. We show that one can compute a fractional solution of the usually non-convex relaxation of the problem which yields an upper bound on the optimum integer solution. Starting from this fractional solution, we employ a deterministic rounding approach which only incurs a small loss in terms of objective, thus leading to a PTAS. This technique can be applied to other previously studied variants of the max-sum dispersion function, including combinations of diversity with linear-score maximization, improving over the previous constant-factor approximation algorithms.

How to mine user-interested path from Web-log is an important and challengeable research topic. On the analysis of the present algorithm's advantages and disadvantages, we propose a new algorithm for discovering such expected Web pages. Through computing the probability of the document which is recommended to the user, we can mine user preferred sub-paths. Accordingly, all the sub-paths are merged, and user preferred paths are formed. Experiments showed that it was more precise than previous algorithm. It's suitable for Web site based application, such as to optimize Web site's topological structure or to design personalized services

In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the algebraic equation defining the curve are floating point numbers depending on a set of parameters, i.e., if one wants to explore modular properties of Riemann surfaces as in the examples discussed below. An additional problem in this context can be computing time since the computation of the Riemann matrix uses the somewhat slow Maple integration routing. Thus, a more efficient computation of the Riemann matrix is interesting if one wants to study families of Riemann surfaces or higher genus examples which are computationally expensive.KeywordsRiemann SurfaceBranch PointTheta FunctionAlgebraic CurveAlgebraic CurfThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We describe an efficient algorithm for maintaining a minimum spanning tree (MST) in a graph subject to a sequence of edge weight modifications. The sequence of minimum spanning trees is computed offline, after the sequence of modifications is known. The algorithm performs O(log n) work per modification, where n is the number of vertices in the graph. We use our techniques to solve the offline geometric MST problem for a planar point set subject to insertions and deletions; our algorithm for this problem performs O(log2n) work per modification. No previous dynamic geometric MST algorithm was known.

Implicit Surface-Based Geometric Fusion

Objectives: This paper presents a new proposed algorithm which performs an efficient modular multiplication method which is advantage because of its reduction in hardware and software. This proposed method implies a systematic approach which increases the parallelism level when compared to the previous versions. Methods/Analysis: Two conventional methods are effectively used to find the modular multiplication output. The previous work effectively combines the first conventional and next two algorithms which are invented to overcome the disadvantages of the first two algorithms. The proposed method effectively eliminates one conventional method. Findings: This process reduces the number of iterations hence, reducing the time consumption required to synthesis the entire algorithm. Thus, the above mentioned method efficiently condenses the hardware utilization for implementing the conventional and previous algorithm so far practiced before. Application/Improvements: This paper replaces the classical algorithm by other method which effectively reduces the number of iterations. This reduction in computation makes a drastic reduction in hardware and time delay to execute the algorithms. This paper shows a modification in the existing parallelism method which further shows a great improvement in reduction of hardware and time delay.

Modeling and solving a Crew Assignment Problem in air transportation

Data driven robust optimization for handling uncertainty in supply chain planning models

In this paper, we develop an efficient characteristic finite element method (FEM) for solving the magnetic induction equation in magnetohydrodynamics (MHD). We carry out numerical experiments on a two dimensional test case to investigate the influence of resistivity at different scales. In particular, our numerical results exhibit how the topological structure and energy of the magnetic field evolve for different scales of resistivity. Magnetic reconnection can also be observed in the numerical experiments.

In this paper, we generalize the efficient geometric ICA algorithm FastGeo to overcomplete settings with more sources than sensors. The solution to this underdetermined problem will be presented in a two step approach. With geometric ICA we get an efficient method for the step--matrix-recovery--while the second step--source-recovery-- uses a maximum-likelihood approach.