BCube is a recursive structure so that:

• BCube($$0$$) is a $$n$$-port switch connects $$n$$ servers
• BCube($$k$$) consists of $$n$$ units of BCube($$k-1$$) and $$n^k$$ units of $$n$$-port switch, in total $$n^{k+1}$$ servers and $$(k+1)n^k$$ switches

Building BCube($$k$$) from BCube($$k-1$$) are as follows: We number the BCube($$k-1$$) from $$1$$ to $$n$$ and in each BCube($$k-1$$), number the server from 1 to $$n^k$$. Then, considering the $$n$$ switches in the layer $$k$$, we connect the $$i$$-th server in $$j$$-th BCube($$k-1$$) to the $$j$$-th port of the $$i$$-th switch.

## Bibliographic data

@inproceedings{
title = "BCube: A High Performance, Server-centric Network Architecture for Modular Data Centers",
author = "Chuanxiong Guo and Guohan Lu and Dan Li and Haitao Wu and Xuan Zhang and Yunfeng Shi and Chen Tian and Yongguang Zhang and Songwu Lu",
booktitle = "Proc. SIGCOMM'09",
pages = "63--74",
month = "August 17–21",
year = "2009",
}