• Journal of the Korean Operations Research and Management Science Society
• /
• v.21 no.3
• /
• pp.63-74
• /
• 1996

Ordering plays an important role in solving an LP problem with sparse matrix by the interior point method. Since ordering is NP-complete, we try to find an efficient method. The objective of this paper is to present an efficient heuristic ordering method for implementation of the minimum deficiency method. Both the ordering method and the data structure play important roles in implementation. First we define a new heuristic pseudo-deficiency ordering method and a data structure for the method-quotient graph and cliqued storage. Next we show an experimental result in terms of time and nonzero numbers by NETLIB problems.

• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.2
• /
• pp.47-56
• /
• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Korean Management Science Review
• /
• v.12 no.2
• /
• pp.31-42
• /
• 1995

The ordering method is used to reduce the fill-ins in interior point methods. In ordering, the data structure plays an important role. In this paper, first, we compare the efficiency and the memory storage requirement of the quotient graph structure and the clique storage. Next, we propose a method of reducing the number of cliques and a data structure for clique storage. Finally, we apply a method of merging rows and absorbing cliques and show the experimental results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.2
• /
• pp.29-43
• /
• 2005

We consider a surface reconstruction problem from geometrical points (i.e., points given without any order) distributed on a series of smooth parallel cross sections in ${\mathbb{R}}^3$. To solve the problem, we utilize the natural points ordering method in ${\mathbb{R}}^2$, described in [18], which is a method of reconstructing a curve from a set of sample points and is based on the concept of diffusion motions of a small object from one point to the other point. With only the information of the positions of these geometrical points, we construct an acceptable surface consisting of triangular facets using a heuristic algorithm to link a pair of parallel cross-sections constructed via the natural points ordering method. We show numerical simulations for the proposed algorithm with some sets of sample points.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.7A
• /
• pp.1036-1045
• /
• 1999

In this paper, we proposed a causal ordering algorithms which is efficiently applicable to overlapped process group environments where one process may belong to several process groups. The ones is proposed to choose with topology of the network. We proposed receiver select algorithm in broadcast network, sender select algorithm in point-to-point network. Each algorithms removes unnecessary vector timestampes to reduce the message overhead required for the causual ordering. And, compressed vector timestamps using the locally maintained vector timestamp information of other processes and other groups to minimize the message overhead. Also, we logically proved the proposed causal ordering method, and compared the performance of the proposed algorithm with ones of other existing algorithms by computer simulation.

• International Journal of Contents
• /
• v.11 no.2
• /
• pp.9-14
• /
• 2015

We propose a new distance measure between 2-dimensional points to provide a total order for an entire point set and to reflect the correct geometric meaning of the naturalness of the point ordering. In general, there is no total order for 2-dimensional point sets, so curve reconstruction algorithms do not solve the self-intersection problem because the distance used in the previous methods is the Euclidean distance. A natural distance based on Brownian motion was previously proposed to solve the self-intersection problem. However, the distance reflects the wrong geometric meaning of the naturalness. In this paper, we correct the disadvantage of the natural distance by introducing a polar-natural distance, and we also propose a new curve reconstruction algorithm that is based on the polar-natural distance. Our experiments show that the new distance adequately reflects the correct geometric meaning, so non-simple curve reconstruction can be solved.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.3 no.2
• /
• pp.120-125
• /
• 2002

In this paper, we propose a new ordering model for the mixed parts transportation problem with multi-items based on the depot system. Order scale are used as decision parameters instead of order point for ordering multi-items. Finally we test the model with simple example and show computational result that verifies the effectiveness of the model.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.37 no.2
• /
• pp.55-64
• /
• 2000

In this paper, we propose an efficient datapath placement algorithm to minimize track density. Here, we consider each datapath element as a cluster, and merge the most strongly connected two clusters to a new cluster until only one cluster remains. As nodes in the two clusters to be merged are already linearly ordered respectively, we can merge two clusters with connecting them. The proposed algorithm produces circular linear ordering by connecting starting point and end point of the final cluster, and n different linear ordering by cutting between two contiguous elements of the circular linear ordering. Among the n different linear ordering, the linear ordering to minimize track density is final solution. In this paper, we show and utilize that if two clusters are strongly connected in a graph, the inner product of the corresponding vectors mapped in d-dimensional space using spectral method is maximum. Compared with previous datapath placement algorithm GA/S $A^{［2］}$, the proposed algorithm gives similar results with much less computation time.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.283-296
• /
• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.28 no.1
• /
• pp.51-61
• /
• 2003

In the normal equations approach in which the ordering and factorization phases are separated, the factorization in the augmented system approach is computed dynamically. This means that in the augmented system the numerical factorization should be performed to obtain the non-zero structure of Cholesky factor L. This causes much time to set up the non-zero structure of Cholesky factor L. So, we present a method which can separate the ordering and numerical factorization in the augmented system. Experimental results show that the proposed method reduces the time for obtaining the non-zero structure of Cholesky factor L.