• The Journal of Korean Association of Computer Education
• /
• v.13 no.5
• /
• pp.91-102
• /
• 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 Korean Institute of Information and Commucation Sciences Conference
• /
• 2017.05a
• /
• pp.321-324
• /
• 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.

• The Transactions of the Korea Information Processing Society
• /
• v.5 no.10
• /
• pp.2615-2626
• /
• 1998

In this paper, we propose a new interconnection network called RFM graph, whichis the merger of the directed rotator and Faber-Moore graph, and analyze fault tolerance, routing algorithm node disjoint cycles and broadcasting algorithm. We also describe methods to embed star graph, 2 dimesional torus and bubblesort graph into RFM graph with unit expasion and dilation 2.

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

• Journal of Korea Multimedia Society
• /
• v.17 no.6
• /
• pp.725-732
• /
• 2014

The Pancake graph is node symmetric and useful interconnection network in the field of data sorting algorithm. The Half Pancake graph is a new interconnection network that reduces the degree of the Pancake graph by approximately half and improves the network cost of the Pancake graph. In this paper, we analyze topological properties of the Half Pancake graph $HP_n$. Fist, we prove that $HP_n$ has maximally fault tolerance and recursive scalability. In addition, we show that in $HP_n$, there are isomorphic graphs of low-dimensional $HP_n$. Also, we propose that the Bubblesort $B_n$ can be embedded into Half Pancake $HP_n$ with dilation 5, expansion 1. These results mean that various algorithms designed for the Pancake graph and the Bubble sort graph can be executed on $HP_n$ efficiently.