近年來，隨著網路直播與視訊串流需求的增加，群播 (IP multicast) 技術變得越來越熱門。群播可以實現發送端傳送一個群播訊息；訊息可以在路徑分岔處的交換機或路由器被複製；最後所有的接收端都收到訊息。然而，在傳統網絡中，群播需要特殊的高性能硬件來支持 IGMP、PIM、MBGP 和 MSDP ... 等協議。由於群播協議會產生大量開銷並且有時會降低網絡效能，因此即使支持群播，傳統網絡中也經常會關閉它。然而，這些群播的缺點可以在軟件定義網絡（software defined networking, SDN）中克服。在 SDN 中，OpenFlow group 實現了群播和多路徑路由。有了多路徑路由，每個目標的吞吐量可以大於單個路徑的帶寬。
在本篇論文中，我們提出了一種基於單播的多路徑群播路由演算法，我們稱之為Maximum Concurrent Multicast Flow algorithm (MCMF)，以確保可以達到接收端的最小速率要求。 MCMF 的主要概念是藉由遞迴地將圖劃分為子圖，從而將多播多路徑路由問題簡化為多商品流問題，使得子圖可以本質上由多商品流問題解決。我們的實驗結果顯示我們的方法在吞吐量和延遲方面都比 SDN 中的傳統群播路由演算法具有更好的性能。

In recent years, with the increase in demand for live streaming and video streaming, IP multicasting becomes a popular issue. IP multicasting allows a source to send only one copy of a multicast message; copies of the message is made only at the switches/routers where paths diverge; and eventually all destinations receive the message. However, in traditional networking, IP multicasting requires specific high performance hardware that supports IP multicast protocols such as IGMP, PIM, BGMP, and MSDP. Since the IP multicast protocols incur large overhead and sometimes degrade network performance, IP multicasting is often turned off in traditional networking even when it is supported. However, these disadvantages of IP multicasting can be overcome in software defined networks (SDNs). In SDNs, OpenFlow groups facilitate both IP multicasting and multipath routing. With multipath routing, the per-destination throughput can be greater than the bandwidth of a the single path.
In this thesis, we proposed a multicast multipath routing algorithm based on unicast called Maximum Concurrent Multicast Flow algorithm (MCMF), which guarantees to achieve the minimum rate requirements of the destinations. The main idea of MCMF is to reduce the multicast multipath routing problem into the multi-commodity flow problem by recursively partitioning the graph into sub-graphs such that the sub-graphs can be essentially solved by the multi-commodity flow problem. Our experiment results show that our method has better performance than traditional multicast routing algorithms in SDN in terms of both throughput and latency.

[1] N. McKeown, T. Anderson, H. Balakrishnan, et al., “Openflow: Enabling in-
novation in campus networks,” SIGCOMM Comput. Commun. Rev., vol. 38,
no. 2, pp. 69–74, Mar. 2008.
[2] L. Li, G. Oikonomou, M. Beach, R. Nejabati, and D. Simeonidou, “An sdn
agent-enabled rate adaptation framework for wlan,” in ICC 2019 - 2019
IEEE International Conference on Communications (ICC), 2019, pp. 1–6.
[3] U. Adams, “Ry ̄u: Fast float-to-string conversion,” in Proceedings of the 39th
ACM SIGPLAN Conference on Programming Language Design and Imple-
mentation, ser. PLDI 2018, Philadelphia, PA, USA: Association for Com-
puting Machinery, 2018, pp. 270–282.
[4] Floodlight openflow controller, https://groups.io/g/floodlight, [Online;
accessed 15-July-2022].
[5] J. Medved, R. Varga, A. Tkacik, and K. Gray, “Opendaylight: Towards a
model-driven sdn controller architecture,” in Proceeding of IEEE Interna-
tional Symposium on a World of Wireless, Mobile and Multimedia Networks
2014, 2014, pp. 1–6.
[6] Open network operating system (onos), https://docs.onosproject.org/,
[Online; accessed 15-July-2022].
[7] P. Bosshart, D. Daly, G. Gibb, et al., “P4: Programming protocol-independent
packet processors,” SIGCOMM Comput. Commun. Rev., vol. 44, no. 3,
pp. 87–95, Jul. 2014.
[8] S. Bhattacharyya, “An overview of source-specific multicast (ssm),” RFC
Editor, RFC 3569, Jul. 2003, http://www.rfc-editor.org/rfc/rfc3569.
txt. [Online]. Available: http://www.rfc-editor.org/rfc/rfc3569.txt.
[9] B. Fenner, M. Handley, H. Holbrook, et al., “Protocol independent multicast
- sparse mode (pim-sm): Protocol specification (revised),” RFC Editor, STD
83, Mar. 2016.
[10] E. Akin and T. Korkmaz, “Rate-based dynamic shortest path algorithm for
efficiently routing multiple flows in sdn,” in ICC 2019 - 2019 IEEE Inter-
national Conference on Communications (ICC), 2019, pp. 1–7.
[11] S. Afzal, V. Testoni, J. F. F. de Oliveira, C. E. Rothenberg, P. Kolan, and
I. Bouazizif, “A novel scheduling strategy for mmt-based multipath video
streaming,” in 2018 IEEE Global Communications Conference (GLOBE-
COM), 2018, pp. 206–212.
[12] T.-W. Chang, Y.-J. Tang, Y.-S. Chen, W.-H. Hsu, and M.-J. Tsai, “Max-
imum concurrent flow problem in mpls-based software defined networks,”
in 2018 IEEE Global Communications Conference (GLOBECOM), 2018,
pp. 1–7.
[13] N. Garg and J. K ̈onemann, “Faster and simpler algorithms for multicom-
modity flow and other fractional packing problems,” SIAM Journal on Com-
puting, vol. 37, no. 2, pp. 630–652, 2007.
[14] M. T. Ananta, J.-R. Jiang, and M. A. Muslim, “Multicasting with the
extended dijkstra’s shortest path algorithm for software defined network-
ing,” International Journal of Applied Engineering Research, vol. 9, no. 23,
pp. 21 017–21 030, 2014.
[15] C. A. C. Marcondes, T. P. C. Santos, A. P. Godoy, C. C. Viel, and C. A. C.
Teixeira, “Castflow: Clean-slate multicast approach using in-advance path
processing in programmable networks,” in 2012 IEEE Symposium on Com-
puters and Communications (ISCC), 2012, pp. 000 094–000 101.
[16] P. Virtanen, R. Gommers, T. E. Oliphant, et al., “SciPy 1.0: Fundamental
Algorithms for Scientific Computing in Python,” Nature Methods, vol. 17,
pp. 261–272, 2020. doi: 10.1038/s41592-019-0686-2.
[17] A.-.-H. Esfahanian, “Connectivity algorithms,” in Topics in structural graph
theory, Cambridge University Press Cambridge, 2013, pp. 268–281.
[18] Google or-tools, https://developers.google.com/optimization, [Online;
accessed 15-July-2022].
[19] K. Weihe, “Rk ahuja, tl magnanti, jb orlin: Network flows: Theory, algo-
rithms and applications,” ZOR, vol. 41, pp. 252–252, 1995.
[20] NetworkX developer team, Networkx, https : / / networkx . github . io/,
[Online; accessed 4-August-2022].
[21] B. Pfaff, J. Pettit, T. Koponen, et al., “The design and implementation of
open {vswitch},” in 12th USENIX symposium on networked systems design
and implementation (NSDI 15), 2015, pp. 117–130.
[22] R. L. S. de Oliveira, C. M. Schweitzer, A. A. Shinoda, and L. R. Prete,
“Using mininet for emulation and prototyping software-defined networks,”
in 2014 IEEE Colombian Conference on Communications and Computing
(COLCOM), 2014, pp. 1–6.
[23] Smcroute - a static multicast routing daemon, https : / / github . com /
troglobit/smcroute, [Online; accessed 15-July-2022].
[24] E. F. Moore, “The shortest path through a maze,” in Proc. Internat. Sympos.
Switching Theory 1957, Part II, Harvard Univ. Press, Cambridge, Mass.,
1959, pp. 285–292.
[25] R. C. Prim, “Shortest Connection Networks And Some Generalizations,”
Bell System Technical Journal, vol. 36, no. 6, pp. 1389–1401, Nov. 1957.