• KIPS Transactions on Computer and Communication Systems
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• v.4 no.2
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• pp.37-40
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• 2015

In this paper, we present linear, varied and mixed edge labeling methods using 2-edge labeling on binomial trees. As a result of this paper, we can design the variable topologies to enable optimal broadcasting with binomial tree as spanning tree, if we use these edge labels as the jump sequence of a sort of interconnection networks, circulant graph, with maximum connectivity and high reliability.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.05a
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• pp.195-197
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• 2013

본 논문에서는 이항트리에서의 선형적 에지번호매김방법과 변형된 에지번호매김방법을 제안한다. 이러한 연구결과는 최대 연결도를 갖는 신뢰성이 높은 상호연결망의 일종인 원형군 그래프(circulant graph)의 점프열(jump sequence)로 에지번호들을 사용하면 이항트리를 스패닝 트리로 갖고 최적방송이 가능한 위상설계를 할 수 있다.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.12
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• pp.226-231
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• 2016

Binomial trees are used to price barrier options. Since barrier options are path dependent, option values of each node are calculated from binomial trees using backward induction. We use generalized Catalan numbers to determine the number of cases not reaching a barrier. We will generalize Catalan numbers by imposing upper and lower bounds. Reaching a barrier in binomial trees is determined by the difference between the number of up states and down states. If we count the cases that the differences between the up states and down states remain in a specific range, the probability of not reaching a barrier is obtained at a final node of the tree. With probabilities and option values at the final nodes of the tree, option prices are computable by discounting the expected option value at expiry. Without calculating option values in the middle nodes of binomial trees, option prices are computable only with final option values. We can obtain a probability distribution of exercising an option at expiry. Generalized Catalan numbers are expected to be applicable in many other areas.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.1
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• pp.27-34
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• 2005

In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.479-482
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• 1998

Whether a given tree is a subgraph of the interconnection network topology is one of the important problem in parallel computing. Trees are used as the underlying structure for divide and conquer algorithms and provide the solution spaces for NP-complete problems. Complete binary trees are the basic structure among those trees. Binomial trees play an important role in broadcasting messages in parallel networks. If binomial trees can be efficiently embedded in complex binary trees, broadcasting algorithms can be effeciently performed on the interconnection networks. In this paper, we present average dilation 2 embedding of binomial trees in complete binary trees.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.289-292
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• 1998

Trees are the underlying structure for divide-and-conquer algorithms and the graphs that provide the solution spaces for NP-complete problems. Complete binary trees are the basic structure among trees. Therefore, if complete binary trees can be embedded in binomial trees, the algorithms which are provided by complete binary trees can be performed efficiently on the interconnection networks which have binomial trees as their subgraphs or in which binomial trees can be embedded easily. In this paper, we present dilation 2 embedding of complete binary trees in binomial trees.

• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.167-170
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• 2004

We present a novel graph labeling problem called S-edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be ${ a_n / a_n = 4 a_{n-l}+l,\;a_{n-1}=0}$. We show that every binomial tree is possible S-edge labeling by giving labeling schems to them. The labelings on the binomial trees are applied to their embedings into interconnection networks.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.324-327
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• 2007

유전프로그래밍(GP)은 GA, ES, 그리고 EA등에 비해 구조의 복잡함으로 인해 상대적으로 진화방식 및 진화연산자에 대한 연구가 미진한 실정이다. 본 논문에서는 유전프로그래밍에 대한 점진형 진화 방식과 트리 깊이 및 부모간의 거리를 기반으로 한 새로운 진화연산자를 제안한다. 이항식 벤치마크 문제에 대하여 실험을 수행하였고, 세대형 진화 방식 및 기존 연산자와의 성능을 비교하였다.

• The Journal of the Korea Contents Association
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• v.4 no.4
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• pp.189-196
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• 2004

Most of the recent researches for ATM switches have been based on multistage interconnection network known as regularity and self-routing property. These networks can switch packets simultaneously and in parallel. However, they are blocking networks in the sense that packet is capable of collision with each other Mainly Banyan network have been used for structure. There are several ways to reduce the blocking or to increase the throughput of banyan-type switches: increasing the internal link speeds, placing buffers in each switching node, using multiple path, distributing the load evenly in front of the banyan network and so on. Therefore, this paper proposes the use of recirculating shuffle-exchange network to reduce the blocking and to improve hardware complexity. This structures are recirculating shuffle-exchange network as simplified in hardware complexity and Rank network with tree structure which send only a packet with highest priority to the next network, and recirculate the others to the previous network. after it decides priority number on the Packets transferred to the same destination, The transferred Packets into banyan network use the function of self routing through decomposition and composition algorithm and all they arrive at final destinations. To analyze throughput, waiting time and packet loss ratio according to the size of buffer, the probabilities are modeled by a binomial distribution of packet arrival. If it is 50 percentage of load, the size of buffer is more than 15. It means the acceptable packet loss ratio. Therefore, this paper simplify the hardware complexity as use of recirculating shuffle-exchange network instead of bitonic sorter.