• 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.

• Proceedings of the Korea Contents Association Conference
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• 2014.11a
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• pp.293-294
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• 2014

정보 검색 분야에서 키 탐색을 빠르게 하기 위한 인덱스 구조로 이진 트라이가 대표적으로 사용된다. CB 트리는 이진 트라이 구조를 구현할 경우 발생하는 저장 공간의 부담을 축소하기 위해 이진 시퀀스를 사용하여 저장한다. 이는 저장 공간 측면에서 상당한 우수성을 보여주나 키의 잦은 삽입 및 삭제 요구가 있을 경우 이진 비트열에 대한 시프트 연산이 요구되는 부담이 있다. 본 논문에서는 완전 이진 트라이 구조를 사용하여 CB 트리를 표현하는 방법을 제시하였다. 저장 공간의 크기가 증가되기는 하지만 키가 삽입되거나 삭제되어도 이진 비트열에 대한 시프트 연산이 필요하지 않은 장점이 있다.

• 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 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.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:Information Networking
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• v.36 no.1
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• pp.57-67
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• 2009

Packet forwarding in the Internet routers is to find out the longest prefix that matches the destination address of an input packet and to forward the input packet to the output port designated by the longest matched prefix. The IP address lookup is the key of the packet forwarding, and it is required to have efficient data structures and search algorithms to provide the high-speed lookup performance. In this paper, an efficient IP address lookup algorithm using binary search is investigated. Most of the existing binary search algorithms are not efficient in search performance since they do not provide a balanced search. The proposed binary search algorithm performs perfectly balanced binary search using switch pointers. The performance of the proposed algorithm is evaluated using actual backbone routing data and it is shown that the proposed algorithm provides very good search performance without increasing the memory amount storing the forwarding table. The proposed algorithm also provides very good scalability since it can be easily extended for multi-way search and for large forwarding tables

• 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 Korea Institutes of Information Security and Cryptology Conference
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• 2002.11a
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• pp.77-80
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• 2002

그룹에 속한 멤버들만이 통신하고자 하는 그룹웨어 응용프로그램이 보안상 중요한 문제로 인식되면서, 그룹키를 안전하게 생성하여 나누어 갖는 것이 필요하게 되었다. 본 논문은 어떤 그룹에 속한 모든 멤버들이 잘 알려진 두 멤버간의 Diffie-Hellman의 키 교환 프로토콜을 이용하여, 모든 메시지들을 안전하게 전달함으로써 그룹키를 나누어 갖는 새로운 그룹키 동의 프로토콜을 제안한다. 이 프로토콜은 완전 이진 트리를 이용하여 기존의 많은 양의 모듈러 멱승 연산을 일부 곱셈 연산으로 전환함으로써, 그룹키를 만드는데 있이 모듈러 멱승 계산량을 줄이는데 효과적이다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.11B
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• pp.911-919
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• 2004

IP address lookup is one of the essential functions on internet routers, and it determines overall router performance. The most important evaluation factor for software-based IP address lookup is the number of the worst case memory accesses. Binary prefix tree (BPT) scheme gives small number of worst case memory accesses among previous software-based schemes. However the tree structure of BPT is normally unbalanced. In this paper, we propose weighted binary prefix tree (WBP) scheme which generates nearly balanced tree, through combining the concept of weight to the BPT generation process. The proposed WBPT gives very small number of worst case memory accesses compared to the previous software-based schemes. Moreover the WBPT requires comparably small size of memory which can be fit within L2 cache for about 30,000 prefixes, and it is rather simple for prefix addition and deletion. Hence the proposed WBPT can be used for software-based If address lookup in practical routers.