Completely Independent Spanning Trees on BCCC Data Center Networks With an Application to Fault-Tolerant Routing

• Published in: IEEE transactions on parallel and distributed systems Vol. 33; no. 8; pp. 1939 - 1952
• Main Authors: Li, Xiao-Yan, Lin, Wanling, Liu, Ximeng, Lin, Cheng-Kuan, Pai, Kung-Jui, Chang, Jou-Ming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Algorithms; Apexes; BCube connected crossbars (BCCC); Commodities; Completely independent spanning trees (CISTs); compound graphs; Compounds; Computer centers; data center networks (DCNs); Data centers; Fault tolerance; Fault tolerant systems; Graph theory; Interface cards; Network interface cards; Network latency; Performance evaluation; Routing; Routing (telecommunications); server-centric DCNs; Servers; Switches; Trees (mathematics)
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2021.3133595

A set of <inline-formula><tex-math notation="LaTeX">k</tex-math> <mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq1-3133595.gif"/> </inline-formula> spanning trees in a graph <inline-formula><tex-math notation="LaTeX">G</tex-math> <mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq2-3133595.gif"/> </inline-formula> are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices <inline-formula><tex-math notation="LaTeX">x</tex-math> <mml:math><mml:mi>x</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq3-3133595.gif"/> </inline-formula> and <inline-formula><tex-math notation="LaTeX">y</tex-math> <mml:math><mml:mi>y</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq4-3133595.gif"/> </inline-formula> in any two trees have neither vertex nor edge in common, except for <inline-formula><tex-math notation="LaTeX">x</tex-math> <mml:math><mml:mi>x</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq5-3133595.gif"/> </inline-formula> and <inline-formula><tex-math notation="LaTeX">y</tex-math> <mml:math><mml:mi>y</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq6-3133595.gif"/> </inline-formula>. The existence of multiple CISTs in the underlying graph of a network has applications in fault-tolerant broadcasting and secure message distribution. In this paper, we investigate the construction of CISTs in a server-centric data center network called BCube connected crossbars (BCCC), which can provide good network performance using inexpensive commodity off-the-shelf switches and commodity servers with only two network interface card (NIC) ports. The significant advantages of BCCC are its good expandability, lower communication latency, and higher robustness in component failure. Based on the structure of compound graphs of BCCC, we provide efficient algorithms to construct <inline-formula><tex-math notation="LaTeX">\lceil \frac{n}{4}\rceil</tex-math> <mml:math><mml:mrow><mml:mo>⌈</mml:mo><mml:mfrac><mml:mi>n</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>⌉</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chang-ieq7-3133595.gif"/> </inline-formula> CISTs in the logical graph of BCCC, denoted by <inline-formula><tex-math notation="LaTeX">L</tex-math> <mml:math><mml:mi>L</mml:mi></mml:math><inline-graphic xlink:href="chang-ieq8-3133595.gif"/> </inline-formula>-<inline-formula><tex-math notation="LaTeX">BCCC(n,k)</tex-math> <mml:math><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chang-ieq9-3133595.gif"/> </inline-formula>, for <inline-formula><tex-math notation="LaTeX">n\geqslant 5</tex-math> <mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mi>⩾</mml:mi><mml:mn>5</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="chang-ieq10-3133595.gif"/> </inline-formula>. As a by-product, we obtain a fault-tolerant routing that takes the constructed CISTs as its routing table. We then evaluate the performance of the fault-tolerant routing through simulation results.