• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.7
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• pp.1327-1334
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• 2017

The Bubble sort graph is node symmetric, and can be used in the data sorting algorithm. In this research we propose and analyze that Half Bubble sort graph that improved the network cost of Bubble sort graph. The Half Bubble sort graph's number of node is n!, and its degree is ${\lfloor}n/2{\rfloor}+1$. The Half Bubble sort graph's degree is $${\sim_=}0.5$$ times of the Bubble sort, and diameter is $${\sim_=}0.9$$ times of the Bubble sort. The network cost of the Bubble sort graph is $${\sim_=}0.5n^3$$, and the network cost of the half Bubble sort graph is $${\sim_=}0.2n^3$$. We have proved that half bubble sort graph is a sub graph of the bubble sort graph. In addition, we proposed a routing algorithm and analyzed the diameter. Finally, network cost is compared with the bubble sort graph.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.05a
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• pp.321-324
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• 2017

Bubblesort graph is mathematically modeled with bubbling methods, which can arrange data. Bubblesort graph Bn's degree is n, it's routing path length ${\frac{n(n-1)}{2}}$, and its network cost is $O(n^3)$. In this paper we suggest the number of Bubblesort graph's degree reduced to half as a solution to improve the network cost of Bubblesort graph. The Bubblesort graph which has the following restriction is a connected graph randomly from node U to node V for routing.

• Proceedings of the Korea Information Processing Society Conference
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• 2008.05a
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• pp.601-604
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• 2008

전위그래프와 버블정렬그래프는 스타그래프가 갖는 노드대칭성, 재귀적구조, 최대 고장허용도 등 그래프이론 관점에서 좋은 성질을 갖는 상호연결망이다. 본 논문에서는 버블정렬(bubblesort)그래프 $B_n$와 버블정렬-스타(bubblesort star)그래프가 전위(Transposition) 그래프 $T_n$의 서브그래프임을 보인다. 또한, 전위(Transposition)그래프 $T_n$을 버블정렬(Bubblesort)그래프 $B_n$으로 임베딩하는 연장율이 O(n)임을 보인다.

• The Journal of Korean Association of Computer Education
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• v.13 no.5
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• pp.91-102
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• 2010

Star graph is a well-known interconnection network to further improve the network cost of Hypercube and has good properties such as node symmetry, maximal fault tolerance and strongly hierarchical property. In this study, we will suggest embedding scheme among star graph and pancake graph, bubblesort graph, which are variations of star graph. We will show that bubblesort graph can be embedded into pancake and star graph with dilation 3, expansion 1, respectively and pancake graph can be embedded into bubblesort graph with dilation cost O($n^2$). Additionally, we will show that star graph can be embedded into pancake graph with dilation 4, expansion 1. Also, with dilation cost O(n) we will prove that star graph can be embedded into bubblesort graph and pancake graph can be embedded into star graph.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.04a
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• pp.111-114
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• 2010

스타 그래프, 버블정렬 그래프, 팬케익 그래프는 노드 대칭성(node symmetric), 최대 고장 허용도(maximum fault tolerance), 계층적 분할 성질을 갖고, 하이퍼큐브보다 망비용이 개선된 상호 연결망이다. 본 연구에서는 상호연결망으로 널리 알려진 스타 그래프와 그의 변형된 그래프들 사이의 임베딩 방법을 제안하고, 임베딩 비용을 분석한다. 임베딩 결과는 버블정렬 그래프는 스타 그래프에 연장율(dilation) 3, 스타그래프는 팬케익 그래프에 연장율 4로 각각 임베딩 가능하다.

• Proceedings of the Korea Information Processing Society Conference
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• 2008.05a
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• pp.597-600
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• 2008

스타(star) 네트워크는 노드 대칭성, 최대 고장 허용도, 계층적 분할 성질을 갖고, 하이퍼큐브보다 망 비용이 개선 된 상호 연결망이다. 본 연구에서는 상호연결망으로 널리 알려진 스타네트워크와 RFM, 버블정렬네트워크 사이의 임베딩 방법을 제안하고, 임베딩의 연장율 비용을 분석한다. 연구 결과로 버블정렬(Bubblesort) 그래프 $B_N$을 RFM 그래프 $R_N$에 연장비율 2, 버블정렬(Bubblesort) 그래프 $B_N$을 스타그래프 $S_N$에 연장율 3에 임베딩 할 수 있다.