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Tsinghua Science and Technology  2019, Vol. 24 Issue (2): 147-159    doi: 10.26599/TST.2018.9010072
Minimum-Cost Forest for Uncertain Multicast with Delay Constraints
Bangbang Ren, Geyao Cheng*, Deke Guo
∙ Bangbang Ren, Geyao Cheng, and Deke Guo are with the College of Systems Engineering, National University of Denfense Technology, Changsha 410072, China. E-mail:,
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The use of multicast transmission can efficiently reduce the consumption of network resources by jointly serving multiple destinations with a single source node. Currently, many multicast applications impose the constraint wherein multicast flows must be processed by a series of Virtual Network Functions (VNFs) before reaching their destinations. Given a multicast transmission, there are usually multiple server nodes, each of which is able to host all the required VNFs. Thus, the multicast flow should be initially steered to one or a few selected server nodes that act as pseudo sources, and the destinations will then retrieve new flow from any of these pseudo sources. In this paper, we model this kind of multicast as an uncertain multicast with multiple pseudo sources, whose routing structure is usually a forest consisting of multiple isolated trees. We then characterize and construct the Delay-guaranteed Minimum Cost Forest (D-MCF) such that each path from the source to the destination satisfies the end-to-end delay constraint. To tackle this NP-hard problem, we design two efficient methods, the Partition Algorithm (PA) and the Combination Algorithm (CA), to approximate the optimal solution. Theoretical analyses and evaluations indicate that these two methods can generate the desired routing forest for any multicast transfer. Moreover, the PA method achieves a better balance between performance and time consumption than the CA method. The evaluation results show that PA-(Ω+20) can reduce total cost by 49.02% while consuming 12.59% more time, thus significantly outperforming the CA-(Ω+20) method.

Key wordsuncertain multicast      network function virtualization      delay guaranteed     
Received: 13 May 2017      Published: 29 April 2019
Corresponding Authors: Geyao Cheng   
About author:

Deke Guo received the BS degree from Beijing University of Aeronautics and Astronautics in 2001, and the PhD degree from National University of Defense Technology in 2008. He is currently a professor in the College of Systems Engineering at National University of Defense Technology. His research interests include distributed systems, software-defined networking, data center networking, wireless and mobile systems, and interconnection networks. He is a senior member of the IEEE and a member of the ACM.

Cite this article:

Bangbang Ren, Geyao Cheng, Deke Guo. Minimum-Cost Forest for Uncertain Multicast with Delay Constraints. Tsinghua Science and Technology, 2019, 24(2): 147-159.

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Fig. 1 An illustrative example of an uncertain multicast group δ = (S, D) in a network G = (V, E, c, d), with source node R, pseudo source nodes S = {F, L}, and destinations D = {A, B, C, G, H, I, J, K}.
Fig. 2 Three routing forests for an uncertain multicast under different delay bounds.
Fig. 3 Illustrative examples of the combination of two multicast trees.
Fig. 4 Changing trends of three metrics when n ranges from 100 to 300 under different forest building methods.
Fig. 5 Changing trends of three metrics when the number of destination ranges from 45 to 105 with |S| = 3 under different forest building methods.
Fig. 6 Changing trends of three metrics when the number of pseudo sources ranges from 1 to 5 with |S|+|D|=120 under different forest building methods.
Fig. 7 Comparisons of routing forests under different settings of the delay bounds.
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