• Title/Summary/Keyword: acyclic

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Coincidences of composites of u.s.c. maps on h-spaces and applications

  • Park, Seh-Ie;Kim, Hoon-Joo
    • Journal of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.251-264
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    • 1995
  • Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

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(1,λ)-EMBEDDED GRAPHS AND THE ACYCLIC EDGE CHOOSABILITY

  • Zhang, Xin;Liu, Guizhen;Wu, Jian-Liang
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.573-580
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    • 2012
  • A (1, ${\lambda}$)-embedded graph is a graph that can be embedded on a surface with Euler characteristic ${\lambda}$ so that each edge is crossed by at most one other edge. A graph $G$ is called ${\alpha}$-linear if there exists an integral constant ${\beta}$ such that $e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}$ for each $G^{\prime}{\subseteq}G$. In this paper, it is shown that every (1, ${\lambda}$)-embedded graph $G$ is 4-linear for all possible ${\lambda}$, and is acyclicly edge-($3{\Delta}(G)+70$)-choosable for ${\lambda}$ = 1, 2.

Knowledge Representation Using Decision Trees Constructed Based on Binary Splits

  • Azad, Mohammad
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.14 no.10
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    • pp.4007-4024
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    • 2020
  • It is tremendously important to construct decision trees to use as a tool for knowledge representation from a given decision table. However, the usual algorithms may split the decision table based on each value, which is not efficient for numerical attributes. The methodology of this paper is to split the given decision table into binary groups as like the CART algorithm, that uses binary split to work for both categorical and numerical attributes. The difference is that it uses split for each attribute established by the directed acyclic graph in a dynamic programming fashion whereas, the CART uses binary split among all considered attributes in a greedy fashion. The aim of this paper is to study the effect of binary splits in comparison with each value splits when building the decision trees. Such effect can be studied by comparing the number of nodes, local and global misclassification rate among the constructed decision trees based on three proposed algorithms.

An Optimal Algorithm for Maximum Origin Destination Flow Path in the Transportation Network (수송 네트워크에서 최대물동량경로 문제의 최적해법)

  • 성기석;박순달
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.1
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    • pp.1-12
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    • 1991
  • This paper studies an optimal algorithm for the Maximum Origin-Destination Flor Path (MODFP) in an acyclic transportation network. We define a Pseudo-Flow each are so that it can give an upper bound to the total flow of a given path. And using the K-th Shortest Path algorithm we obtain upper bound of MODF which is decreasing as the number of searched path grows. Computational Complexity of optimal algorithm is O(K + m) $n_{2}$), K being the total number of searched path. We proved that the problem complexity of finding MODFP in an acyclic network is NP-hard, showing that the-satisfiability problem can be polynomialy reduced to this problem. And we estimated the average of the number K as being (m/n)$^{1,08}$ Exp (0.00689gm) from the computational experiments.

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A Study on the Solution Method of Maximum Origin-Destination Flow Path in an Acyclic Network using Branch and Bound Method (분지한계기법을 이용한 무환네트위크에서 최대물동량경로의 해법에 관한 연구)

  • 성기석;임준목
    • Journal of the Korean Operations Research and Management Science Society
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    • v.20 no.3
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    • pp.31-41
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    • 1995
  • The maximum Origin-Destination Flow Path Problem (MODFP) in an Acyclic Network has known as NP-hard. K. S. Sung has suggested on Optimal Algorithm for MODFP based on the Pseudo flo or arc and the K-th shortest path algorithm. When we try to solve MODFP problem by general Branch and Bound Method (BBM), the upper and lower bounds of subproblems are so weak that the BBM become very inefficient. Here we utilized the Pseudo flow of arc' for the tight bounds of subproblems so that it can produce an efficient BBM for MODFP problem.

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Acylation of Pyridazinylamines by Acyclic Anhydrides; Synthesis of N-Substituted 3-Amino-6-chloropyridazines (Acyclic Anhydrides를 이용한 피리다진아민의 아실레이션; N-치환된 3-아미노-6-클로로피리다진 유도체의 합성)

  • Park Eun-Hee;Park Myung-Sook
    • YAKHAK HOEJI
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    • v.49 no.1
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    • pp.56-59
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    • 2005
  • We synthesized new N-substituted 3-amino-6-chloropyridazine derivatives which were expected to retain biological activity. All synthetic process from pyridazine to 3-aminopyridazines could be carried out conveniently in high yield. N-Substituted 3-amino-6-chloropyridazine derivatives were prepared through amination and acylation from 3,6-dichloropyridazine. 3-Amino-6-chloropyridazine was prepared from the reaction of 3,6-dichloropyridazine with liquid ammonia under autoclave for 6 hrs. The refluxing of 3-amino-6-chloropyridazine and the corresponding acid anhydride for $1{\sim}2$ hrs afforded the N-substituted 3-amino-6-chloropyridazines. Alkyl chain of N-substituent was prolonged to six carbon (hexanoic acid).

A Linear Clustering Method for the Scheduling of the Directed Acyclic Graph Model with Multiprocessors Using Genetic Algorithm (다중프로세서를 갖는 유방향무환그래프 모델의 스케쥴링을 위한 유전알고리즘을 이용한 선형 클러스터링 해법)

  • Sung, Ki-Seok;Park, Jee-Hyuk
    • Journal of Korean Institute of Industrial Engineers
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    • v.24 no.4
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    • pp.591-600
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    • 1998
  • The scheduling of parallel computing systems consists of two procedures, the assignment of tasks to each available processor and the ordering of tasks in each processor. The assignment procedure is same with a clustering. The clustering is classified into linear or nonlinear according to the precedence relationship of the tasks in each cluster. The parallel computing system can be modeled with a Directed Acyclic Graph(DAG). By the granularity theory, DAG is categorized into Coarse Grain Type(CDAG) and Fine Grain Type(FDAG). We suggest the linear clustering method for the scheduling of CDAG using the genetic algorithm. The method utilizes a properly that the optimal schedule of a CDAG is one of linear clustering. We present the computational comparisons between the suggested method for CDAG and an existing method for the general DAG including CDAG and FDAG.

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A Polynomial Algorithm for the Minimum Spanning Arborescence in Transportation Networks with Bitype Arc Costs (이중비용 네트워크에서의 최소비용 극대방향 나무 해법)

  • Sim, Hyun-Taek;Park, Soon-Dal
    • Journal of Korean Institute of Industrial Engineers
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    • v.16 no.1
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    • pp.17-25
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    • 1990
  • Most of the least cost transportation network design problems are frequently formulated as the minimum spanning arborescence problems in directed networks with bitype are costs. These costs are classified whether the arc is included in the path from the root to a specified node over a given spanning arborescence. We prove that this problem is NP-hard, and develop a polynomial time algorithm for acyclic networks. The probelm in acyclic networks is initially formulated as 0-1 integer programming. Next, we prove that the 0-1 relaxed linear programming has an integral optimum solution by complementary slackness conditions. In this paper, we present an $O(n^2)$ algorithm based on a shortest path algorithm.

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Estimation of a Cyclic or Acyclic Network System Reliability and MTTF by the Monte-Carlo Simulation Method (Monte-Carlo Simulation방법(方法)에 의한 복잡한 System의 신뢰성(信賴性)과 평균수명(平均壽命) 추정(推定))

  • Lee, Chang-Ho
    • Journal of Korean Society for Quality Management
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    • v.10 no.2
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    • pp.18-24
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    • 1982
  • This paper estimates the reliability & mean time to failure (MTIF) of a cyclic or acyclic network system by the Monte-Carlo simulation method. Estimates of MTTF and Reliability become difficult as the complexity of a system increases. The method in this paper finds all simple paths from the given network, and then simulates the reliability of the required time and MTFF by using these paths. Life-times of the components in a network follow some probability distributions (Exponential, Weibull, Normal, Lognormal, etc.). The method, written in Level II. Basic Language, is validated for some simple examples and then estimates the reliability and MTFF of some cyclic network system.

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