• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.381-386
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• 2003

In this paper, we consider the problem of embedding complete binary trees into 3-dimensional meshes. The method of embedding a complete binary tree into 3-dimensional mesh with the link congestion two is considered in [1], and the embedding in [2] shows that a complete binary tree can be embedded into a ,3-dimensional mesh of expansion 1.27. The proposed embedding in this paper shows that a complete binary tree can be embedded into a 3-dimensional mesh of expansion approximately 1.125 with the link congestion one, using the dimensional ordered routing. Such method yields some improved features in terms of minimizing the link congestion or the expansion of embedding comparing to the previous results.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.3
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• pp.149-157
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• 2009

The crossed cube, a variation of the hypercube, possesses a better topological property than the hypercube in its diameter that is about half of that of the hypercube. It has been known that an N-node complete binary tree is a subgraph of an (N+1)-node crossed cube [P. Kulasinghe and S. Bettayeb, 1995]. However, efficient embedding methods have not been known for the case that the number of nodes of the complete binary tree is greater than that of the crossed cube. In this paper, we show that an N-node complete binary tree can be embedded into an M-node crossed cube with dilation 1 and load factor [N/M], N>M$\geq$2. The dilation and load factor is optimal. Our embedding has a property that the tree nodes on the same level are evenly distributed over the crossed cube nodes. The property is especially useful when tree-structured algorithms are processed on a crossed cube in a level-by-level way.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.163-176
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• 2019

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

• 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.

• Journal of Korea Multimedia Society
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• v.20 no.4
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• pp.696-703
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• 2017

In this paper, we show how to design based on solving Sudoku problem that is one of the NP-complete problems like Go. We show how to use greedy method which can minimize depth based on tree expansion and how to apply heuristic algorithm for pruning unnecessary branches. As a result of measuring the performance of the proposed method for solving of Sudoku problems, this method can reduce the number of function call required for solving compared with the method of heuristic algorithm or recursive method, also this method is able to reduce the 46~64 depth rather than simply expanding the tree and is able to pruning unnecessary branches. Therefore, we could see that it can reduce the number of leaf nodes required for the calculation to 6 to 34.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.2
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• pp.169-176
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• 2000

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with primary concern of minimizing link congestion. The authors showed that a complete binary tree with $2^P-1$ nodes can be embedded into a 3-dimensional mesh with optimum size, $2^P$ nodes, if the link congestion is two[14], (More precisely, the link congestion of each dimension is two, two, and one if the dimension-ordered routing is used, and two, one, and one if the dimension-ordered routing is not imposed.) In this paper, we present a scheme to find an embedding of a complete binary tree into a 3-dimensional mesh of size no larger than 1.27 times the optimum with link congestion one while using dimension-ordered routing.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.8
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• pp.361-371
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• 2008

In this paper, the hypercube, hyperpetersen networks, whose degree is increasing in accordance with expansion of number of node and complete binary tree are one-to-one embedded into peterson-torus(PT) network which has fixed degree. The one-to-one embedding has less risk of overload or idle for the processor comparative to one-to-many and many-to-one embedding. For the algorithms which were developed on hypercube or hyperpetersen are used for PT network, it is one-to one embedded at expansion ${\doteqdot}1$, dilation 1.5n+2 and link congestion O(n) not to generate large numbers of idle processor. The complete binary tree is embedded into PT network with link congestion =1, expansion ${\doteqdot}5$ and dilation O(n) to avoid the bottleneck at the wormhole routing system which is not affected by the path length.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.2
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• pp.103-114
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• 2008

Overlay Multicast is a promising approach to overcome the implementation problem of IP multicast. Real time services like Internet broadcasting are provided by the overlay multicast technology due to the complex nature and high cost of IP multicast. To reduce frequent updates of multicast members and to support real time service without delay, we suggest a reliable overlay multicast tree based on members' sojourn probabilities. Path reliabilities from a source to member nodes are considered to maximize the reliability of an overlay multicast tree. The problem is formulated as a binary integer programming with degree and delay bounds. A tabu search heuristic is developed to solve the NP-complete problem. Outstanding results are obtained which is comparable to the optimal solution and applicable in real time.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10a
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• pp.762-764
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• 1998

완전 이진트리의 통신형태를 갖는 분활 정복방식의 알고리즘 병렬 컴퓨터에서 실행시킬 때 작업들을 프로세서에 분배하여 처리하게 되는데 이때 통신 링크의 충돌을 줄이는 것이 전체 실행시간을 단축하는 중요한 요소가 된다. 본 논문에서는, 웜홀 라우팅과 양방향 링크를 지원하는 3차원 메쉬로의 완전 이진트리의 임베딩 문제를 다룬다. 이 임베딩 방법은 순위차원 라우팅을 사용하며 링크 충돌이 없는 방법으로 최적의 임베딩 알고리즘이다.

• Journal of the Korea Institute of Military Science and Technology
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• v.17 no.3
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• pp.358-363
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• 2014

In this paper, we present two constructions of the attribute-based broadcast encryption(ABBE) algorithm. Attribute-based encryption(ABE) algorithm enables an access control mechanism over encrypted data by specifying access policies among private keys and ciphertexts. ABBE algorithm can be used to construct ABE algorithm with revocation mechanism. Revocation has a useful property that revocation can be done without affecting any non-revoked uers. The main difference between our algorithm and the classical ones derived from the complete subtree paradigm which is apt for military hierarchy. Our algorithm improve the efficiency from the previously best ABBE algorithm, in particular, our algorithm allows one to select or revoke users by sending ciphertext of constant size with respect to the number of attributes and by storing logarithm secret key size of the number of users. Therefore, our algorithm can be an option to applications where computation cost is a top priority and can be applied to military technologies in the near future.