• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.4
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• pp.59-66
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• 2004

We define a SG(String Graph) and an ASG(Alive String Graph) to the purpose to do static analysis. For a life and death judgment, we apply the rule to the situation which the stone is included and not included. We define the rules that are SR(String Reduction), ER(Empty Reduction), ET(Edge Transform), and CG(Circular Graph), when the stone is not included. We define the rules that are DESR(Dead Enemy Strings Reduction) and SCSR(Same Color String Reduction), when the stone is included. We evaluate a SG that it is an ASG or not by using rules. And we use APC(Articulation Point Check) nile according to number of articulation points lot a life and death judgment. The performance of our method has been tested on the problem set IGS_31_counted form the Computer Go Test Collection. The test set contains 11,191 Points and 1,123 Strings. We obtain 92.5% accuracy of Points and 95.7% accuracy of Strings.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.1
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• pp.10-17
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• 1993

This paper analyzes succinct graph descriptions and its complexity of connectivity problems on context free graph languages under various restrictions. It defines SNLC(Simple Context Free Node Label Controlled) grammar and presents reduction method that solves graph problems without expanding the hierarchical description. It exemplifies the method by giving efficient solutions to connectivity problems on graphs and presents parallel algorithm for reduction and analyzes the complexity. Its results will help application of desing for NETWORK. CAD. VLSI and other engineering problems.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.57-81
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• 2024

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

• The Mathematical Education
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• v.13 no.3
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• pp.22-32
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• 1975

Matroid와 transversal theory에 관한 연구가 활발하게 진행되고 있다. 이 논문은 circuit matroid가 transversal이 되기 위한 필요 충분 조건을 지적하고 이를 증명한 것이다. 곧 어떤 graph의 circuit matroid가 transversal이 되기 위한 필요 충분 조건은 그 graph가 graph $K_4$거나 $C_{k}$ $^{2}$에 homeomorphic인 subgraph를 포함하지 않은 것이다. 증명의 방법으로는 주로 matroid의 cocircuit의 성질을 사용하여 transversal Matroid의 presentation을 적절하게 적용하고 graph의 reduction과 contraction을 이용한다.

• Journal of the Korean Society of Safety
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• v.31 no.5
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• pp.141-148
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• 2016

There exists required safety integrity level (SIL) to assure safety in accordance with international standards for every electrical / electronics / control equipment or systems with safety related functions. The SIL is allocated from lowest level (level 0) to highest level (level 4). In order to guarantee certain safety level that is internationally acceptable, application of methodology for SIL allocation and demonstration based on related international standards is required. Especially, in case of the SIL allocation method without determining of quantitative tolerable risk, the additional review is needed to check whether it is suitable or not is required. In this study, the quantitative risk reduction model based on the safety integrity allocation results of railway platform screen door system using Risk Graph method has been examined in order to review the suitability of quantitative risk reduction according to allocated safety integrity level.

• The KIPS Transactions:PartA
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• v.9A no.2
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• pp.171-180
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• 2002

The effective and accurate data flow problem analysis uses the dominator tree and DJ graphs. The data flow problem solving is to safely reduce the flow graph to the dominator tree. The flow graph replaces a parse tree and used to accurately reduce either reducible or irreducible flow graph to the dominator tree. In this paper, in order to utilize Tarian's path compress algorithm, the Top node finding algorithm is suggested and the existing delay reduction algorithm is improved using Path compression. The delayed reduction a1gorithm using path compression actually compresses the pathway of the dominator tree by hoisting the node while reducing to delay the DJ graph. Realty, the suggested algorithm had hoisted nodes in 22% and had compressed path in 20%. The compressed dominator tree makes it possible to analyze the effective data flow analysis and brings the improved effect for the complexity of code optimization process with the node hoisting effect of code optimization process.

• Journal of Internet Computing and Services
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• v.6 no.6
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• pp.117-125
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• 2005

The dominator tree presents the dominance frontier from directed graph to the tree. we present the effective algorithm for constructing the dominator tree from arbitrary directed graph. The reducible flow graph was reduced to dominator tree after dominator calculation. And the irreducible flow graph was constructed to dominator-join graph using join-edge information of information table. For reducing the dominator tree from dominator-join graph, we implement the effective sequency reducible algorithm and delay reducible algorithm. As a result of implementation, we can see that the delay reducible algorithm takes less execution time than the sequency reducible algorithm. Therefore, we can reduce the flow graph to dominator tree effectively.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.63-73
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• 1988

In this paper, an algorithm is proposed to evaluate the source-to-terminal reliability, the probability that a source node can communicate with a terminal node, in a probabilistic derected graph. By using Satyanaratana's factoring $theorem^{(7)}$, the original graph can be partitioned into two reduced graphs obtained by contracting and deleting the edge connected to the source node in the probabilistic directed graph. The edge removal proposed in this paper and the general series-parallel reduction can then be applied to the reduced graph. This edge reduction can be applied recursively to the reduced graphs until a source node can be connected to a terminal node by one edge. A computer program which can be applied to evaluating the source-to-terminal reliability in a complex and large network has also been developed.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.787-790
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• 1998

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/all destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithm with O(n min{m, nlogn}) and O(n$^{2}$) running time.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.11-20
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• 1995

A new graph problem is formulated to limit the maximum path length of a general directed graph when a minimal set of vertices together with their incident edges are removed from the graph. An optimal algorithm and a heuristic algorithm are proposed and the proposed heuristic algorithm is shown to be effective through experiments using a collection of graphs obtained from large sequential circuits. The heuristic algorithm is based on a feedback vertex set algorithm based on graph reduction.