Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Symmetric properties and two variants of shuffle-cubes (2110.13645v2)

Published 23 Oct 2021 in math.CO and cs.DM

Abstract: Li et al. in [Inf. Process. Lett. 77 (2001) 35--41] proposed the shuffle cube $SQ_{n}$ as an attractive interconnection network topology for massive parallel and distributed systems. By far, symmetric properties of the shuffle cube remains unknown. In this paper, we show that $SQ_{n}$ is not vertex-transitive for all $n>2$, which is not an appealing property in interconnection networks. To overcome this limitation, two novel vertex-transitive variants of the shuffle-cube, namely simplified shuffle-cube $SSQ_{n}$ and balanced shuffle cube $BSQ_{n}$ are introduced. Then, routing algorithms of $SSQ_{n}$ and $BSQ_{n}$ for all $n>2$ are given respectively. Furthermore, we show that both $SSQ_{n}$ and $BSQ_{n}$ possess Hamiltonian cycle embedding for all $n>2$. Finally, as a by-product, we mend a flaw in the Property 3 in [IEEE Trans. Comput. 46 (1997) 484--490].

Citations (2)

Summary

We haven't generated a summary for this paper yet.