1 Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2 Department of Key Accounts, China Mobile Group Jiangsu Co., Ltd., Nanjing 210029, China;
3 School of Biomedical Engineering and Information, Nanjing Medical University, Nanjing 211166, China

Abstract Network virtualization (NV) is pushed forward by its proponents as a crucial attribute of next generation network, aiming at overcoming the gradual ossification of current networks, particularly to the worldwide Internet. Through virtualization, multiple customized virtual networks (VNs), requested by users, are allowed to coexist on the underlying substrate networks (SNs). In addition, the virtualization scheme contributes to sharing underlying physical resources simultaneously and seamlessly. However, multiple technical issues still stand in the way of NV successful implementation. One key technical issue is virtual network embedding (VNE), known as the resource allocation problem for NV. This paper conducts a survey of embedding algorithms for VNE problem. At first, the NV business model for VNE problem is presented. Then, the latest VNE problem description is presented. Main performance metrics for evaluating embedding algorithms are also involved. Afterwards, existing VNE algorithms are detailed, according to the novel proposed category approach. Next, key future research aspects of embedding algorithms are listed out. Finally, the paper is briefly concluded.

About author: Haotong Cao, received B.S. Degree in Communication Engineering from Nanjing University of Posts and Telecommunications (NJUPT) in 2015. He is currently pursuing his Ph.D. Degree in NJUPT, Nanjing, China. He was a visiting scholar of Loughborough University, U.K. in 2017. He has served as the TPC member of multiple IEEE conferences, such as IEEE INFOCOM, IEEE ICC and IEEE Globecom. He is also serving as the reviewer of multiple academic journals, such as IEEE/ACM Transactions on Networking, IEEE Transactions on Network and Service Management, (Elsevier) Computer Networks and IEEE Networking Letters. He has published multiple IEEE Trans./Journal/Magazine papers since 2016. His research interests include next generation network, wireless communication theory, resource allocation in wired and wireless networks. He was awarded the 2018 Postgraduate National Scholarship of China. He won the Best Paper Award from 2019 IEEE ICC SecSDN Workshop. He is currently a student member of IEEE and IEEE Communications Society. Shengchen Wu, received B.S. Degree in Communication Engineering from Nanjing University of Posts and Telecommunications (NJUPT) in 2012, and M.S. Degree in Electric Computer Engineering from New York University (NYU), USA, in 2014. He is currently pursuing his Ph.D. Degree in the College of Telecommunications and Information Engineering, NJUPT, Nanjing, China. His main research areas include wireless communication technology, Internet of Things technology and applications. He is currently a student member of IEEE and IEEE Communications Society. Yue Hu, received the B.S. Degree in Network Engineering from Nanjing University of Posts and Telecommunications in 2013, the M.S. Degree in Electronic and Communication Engineering from Nanjing University of Posts and Telecommunications, Nanjing, China, in 2016, and the M.S. Degree in Communication Engineering from Melbourne University, Melbourne, Australia, in 2015. She is currently working in China Mobile Communications Group Jiangsu Co., Ltd.. Her research interests include Internet of Things technology. Yun Liu, is a doctoral supervisor at Nanjing Medical University. She is also a doctor of medicine, chief physician and professor. She is now working as a vice president in the First Affiliated Hospital of Nanjing Medical University. Over the years, she has published many academic papers and presided over many medical research projects. She is proficient in early diagnosis and treatment of diabetic complications, especially in the regulation of diabetic drug therapy and the management of chronic complications. Longxiang Yang, is currently with the College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications (NJUPT), Nanjing, China. He is a Full Professor and Doctoral Supervisor of NJUPT. He is also the dean of College of Telecommunications and Information Engineering, NJUPT. He has fulfilled multiple National Natural Science Foundation projects of China. He has authored and co-authored over 200 technical papers published in various journals and conferences. His research interests include cooperative communication, network coding, wireless communication theory, 5G mobile communication systems, ubiquitous networks and Internet of things.

[1] Q. Duan, Y. Yan and A. Vasilakos,“A survey on service-oriented network virtualization towards convergence of networking and cloud computing,” IEEE Trans. Netw. and Serv. Manag., vol. 9, no. 4, pp. 373-5392, Dec. 2012.
[2] J. A. Stanvokic,“Research Directions for the Internet of Things,” IEEE IoT Journal,vol. 1, no. 1, pp.3-9, 2014.
[3] L. Peterson, L. Peterson, S. Shenker and J. Turner,“Overcoming the internet impasse through virtualization,” IEEE Computer, vol. 38, no. 4, pp. 34-41, Apr. 2015.
[4] N. Chowdhury and R. Boutaba,“A Survey of network virtualization,” Elsevier Computer Networks, vol. 54, no. 5, pp. 862-876, 2010.
[5] J. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lonazo, A. Ksoong and J. Zhang,“What will 5G be?,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1065-1082, Jun. 2014.
[6] X. Tao, Y. Han, X. Xu, P. Zhang and V. C. Leung,“Recent advances and future challenges for mobile network virtualization,” Sci. China Inf. Sci., vol. 60, no. 4, pp. 1-12, 2017.
[7] Cisco. Network virtualization: The new building blocks of network design.Available:http://www.cisco.com/en/US/solutions/collateral/ns340/ns517/.
[8] N. Feamster, L. Gao and J. Rexford,“How to lease the internet in your spare time,” ACM SIGCOMM Computer Communication Review, vol. 37, no. 1, pp. 61-64, 2007.
[9] R. Bless and C. Werle,“Network virtualization from a signaling perspective,” in Proc. International Workshop on the Network of the Future (Future-Net’09), Dresden, Germany, 2009.
[10] D. Schwerdel, D. Guntheret al.,“German-lab experimental facility,” Future Internet Symposium (FIS) 2010, 9, 2010.
[11] H. Zhang, P. Dong, W. Quan and B. Hu,“Promoting efficient communication for high-speed railway using smart collaborative networking,” IEEE Wireless Commun., vol. 22, no. 6, pp. 92-97, Dec., 2015.
[12] R. Bless and C. Werle,“Network virtualization from a signaling perspective,” in Proc. International Workshop on the Network of the Future (Future-Net’09), Dresden, Germany, 2009.
[13] A. Fischer, J. Botero, M. Till Beck, H. De Meer,X. Hesselbach,“Virtual network embedding: A survey,”IEEE Commun. Surveys Tuts., vol. 15, no. 4, pp. 1888-1906, 4^{th} Quart. 2013.
[14] D. Andersen.(2002). Theoretical approaches to node assignment.[Online].Available:http://www.cs.cmu.edu/~dga/papers/andersenassign.ps.
[15] A. Belbekkouche, Md. Mahmud Hasan, A. Karmouch,“Resource discovery and allocation in network virtualization,” IEEE Commun. Surveys Tuts., vol. 14, no. 4, pp. 1114-1128, Feb. 2012.
[16] H. Cao, L. Yang, Z. Liu and T. Wu,“Exact solutions of VNE: A survey,” China Commun., vol. 13, no. 6, pp. 48-62, Jun. 2016.
[17] H. Cao, H. Hu, Z. Qu and L. Yang,“Heuristic solution of virtual network embedding: A survey,” China Commun., vol. 15, no. 3, pp. 186-219, Mar. 2018.
[18] M. Yu, J. Rexford, X. Sun, S. Rao and N. Feamster,“A survey of virtual LAN usage in campus networks,” IEEE Commun. Mag., vol. 49, no. 7, pp. 98-103, Jul. 2011.
[19] F. Hartung, N. Niebert, A. Schieder, R. Rembarz, S. Schmid and L. Eggert,“Advances in network-supported media delivery in next-generation mobile systems,” IEEE Commun. Mag., vol. 44, no. 8, pp. 82-89, Aug. 2006.
[20] F. Bannour, S. Souihi and A. Mellouk,“Distributed SDN control: Survey, taxonomy, and challenges,” IEEE Commun. Surveys Tuts., vol. 20, no. 1, pp. 333-354, Mar. 2018.
[21] O. Shehory, K. Sycara, P. Chalasani and S. Jha,“Agent cloning: an approach to agent mobility and resource allocation,” IEEE Commun. Mag., vol. 36, no. 7, pp. 58, 63-67, Jul. 1998.
[22] A. Alshalan, S. Pisharody and D. Huang,“A survey of mobile VPN technologies,” IEEE Commun. Surveys Tuts., vol. 18, no. 2, pp. 1177-1196, Jun. 2016.
[23] J. Herrera and J. Botero,“Resource allocation in NFV: A comprehensive survey,” IEEE Trans. Netw. and Serv. Manag., vol. 13, no. 3, pp. 518-532, Sept. 2016.
[24] D. Mitra, J. A. Morrison, K. G. Ramakrishnan,“VPN designer: A tool for design of multiservice virtual private networks,” Bell Labs Tech. Journal, vol. 3, no. 4, pp. 15-31, Apr. 1998.
[25] S. Abdelwahab, B. Hamdaoui, M. Guizani and T. Znati,“Network function virtualization in 5G,” IEEE Commun. Mag., vol. 54, no. 4, pp. 84-91, Apr. 2016.
[26] S. Bhardwaj, L. Jain,S. Jain,“Cloud computing: A study of infrastructure as a service (iaas),” Int J. Eng.And Information Technology, vol. 2, pp. 60-63, 2010.
[27] L. Acquaviva, P. Bellavista, F. Bosi, A. Corradi, L. Foschini, S. Monti and A. Sabbioni,“NoMISHAP: A nodel middleware support for high availability in multicloud paas,” IEEE Cloud Computing, vol. 4, no. 4, pp. 60-72, Dec. 2017.
[28] R. A. Asaka, G. H. S.Mendes and G. M. D. Ganga,“Factors influencing customer satisfication in software as a service (SaaS): Proposal of a system of performance indicators,” IEEE Latin America Tans., vol. 15, no. 8, pp. 1536-1541, Aug. 2017.
[29] D. Soldani, K. Pentikousis, R. Tafazolli and D. Franceschini,“5G networks: End-to-end architecture,” IEEE Commun. Mag., vol. 52, no. 11, pp. 62-64, Nov. 2014.
[30] N. Abbas, Y. Zhang, A. Taherkordi and T. Skeie,“Mobile edge computing: A Survey,” IEEE IoT Journal,vol. 5, no. 1, pp. 450-465, 2018.
[31] J. Kleinberg,“Approximation algorithms for disjoint path problems,” Ph.D. Dissertation, MIT, Cambridge, MA, 1996.
[32] L. A. Wolsey, Integer Programming [M]. New York: John Wiley & Sons, 1998.
[33] “GLPK (GNU Linear Programming Kit),” Apr. 2018. Available: . 2018. Available: http://www.gnu.org/software/glpk/.
[34] “IBM ILOG Optimization Products,” Apr.2018. Available: www=01.ibm.com/software/websphere/products/optimization.
[35] T. H. Cormen, C. Stein, R. L. Rivest,C. E. Leiserson, Introduction to Algorithms, 2^{nd} ed. New York, NY, USA:McGraw-Hill, 2001.
[36] M. Fukeshima, K. Sugiyama, T. Hasegawa,A. Nakao,“Minimum disclosure routing for network virtualization and its experimental evaluation,” IEEE/ACM Trans. Netw., vol. 21, no. 6, pp. 1839-1851, Dec. 2013.
[37] M. G. Hinchey, R. Sterritt and C. Rouff,“Swarms and swarm intelligence,” Computer, vol. 40, no. 4, pp. 111-113, Apr. 2007.
[38] J. H. Holland, Adaptation in natural and artificial systems. Cambridge, MA, USA: MIT Press, 1992.
[39] D. M.,“Optimization, learning and natural algorithms,” Ph.D. Thesis, Politecnico di Milano, Italy, 1992.
[40] J. Kennedy and R. Eberhart,“Particle swarm optimization,” in Neural Networks, 1995 IEEE International Conference on, pp. 1942-1948.
[41] S. Kirkpatrick, C. D.Gelatt and M. P.Vecchi,“Optimization by simulated annealing,” Science, vol. 220, pp. 671-680, 1983.
[42] F. Glover,“Future paths for integer programming and links to artificial intelligence,” Comput. Oper. Res., vol.13, pp. 533-549, May 1986.
[43] M. Dayarathna, Y. Wen and R. Fan,“Data center energy modelling: A survey,” IEEE Commun. Surveys Tuts., vol. 18, no. 1, pp. 732-794, Mar. 2016.
[44] B. Chun, G. Iannaccone, R. Katz, G. Lee and L. Niccolini,“An energy case for hybrid datacenters,” ACM SIGOPS Operating Systems Review, vol. 44, no. 1, pp. 7680, 2010.
[45] K. Lee, E. Modiano and H. W. Lee,“Cross-layer survivability in WDM-based networks,” IEEE/ACM Trans. Netw., vol. 19, no. 4, pp. 1000-1013, Aug. 2011.
[46] T. Trinh, H. Esaki,C. Aswakul,“Quality of service using careful overbooking for optimal virtual network resource allocation,” in Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), 2011 8^{th} International Conference on, May 2011, pp. 296-299.
[47] F. Chung,“A brief survey of PageRank Algorithms,” IEEE Trans. Netw. Sci. and Engin., vol. 1, no. 1, pp. 38-42, 2014.
[48] L. Kocsis and C. Szepessvari,“Bandit based Monte-Carlo planning,” in Proc. 17^{th} Eur. Conf. Mach. Learn., Berlin, Germany, Germany, Sep. 2006, pp. 282-293.
[49] R. Coulorm,“Efficient selectivity and backup operators in Monte-Carlo tree search,” in Proc. 5^{th} Int. Conf. Comput. Games (CG), Turin, Italy, May 2006, pp. 72-83.
[50] L. Freeman, The development of social network analysis. Empirical Press Vancouver, BC, 2004.
[51] M. Newman, Networks: An Introduction. Oxford University Press, Oxford, UK, 2010.
[52] A. F. Molisch, Wireless Local Area Networks, New York, NY, USA: Wiley-IEEE , 2012.
[53] M. Yu, Y. Yi, J. Rexfordy and M. Chiang,“Rethinking virtual network embedding: substrate support for path splitting and migration,” ACM SIGCOMM Comput. Commun. Rev., vol. 38, no. 2, pp. 17-29, Mar. 2008.
[54] X. Cheng et al.,“Virtual network embedding through topology-aware node ranking,” ACM SIGCOMM Comput. Commun. Rev., vol. 41, no. 2, pp. 38-47, Apr. 2011.
[55] L. Gong, Y. Wen, Z. Zhu and T. Lee,“Revenue-Driven Virtual Network Embedding Based on Global Resource Information,” in Global Communications Conference (GLOBECOM), 2013 IEEE, Dec. 2013, pp. 2294-2299.
[56] M. Feng, J. Liao, J. Wang, S. Qing,Q. Qi,“Topology-aware virtual network embedding based on multiple characteristics,” in2014 IEEE Conference on Communications (ICC), pp. 2956-2962.
[57] P. Zhang, H. Yao and Y.Liu, et al.,“Virtual network embedding based on the degree and clustering coefficient information,” IEEE Access, vol. 4, pp. 8572-8580, 2016.
[58] H. Cao, L. Yang and H. Zhu,“Novel node-ranking approach and multiple topology attributes-based embedding algorithm for single-domain virtual network embedding,” IEEE IoT Journal, vol. 5, no. 1, pp. 108-120, 2018.
[59] M. Feng, L. Zhang, X. Zhu, J. Wang, Q. Qi and J. Liao,“Topology-aware virtual network embedding through the degree,” in2013 National Doctoral Academic Forum on Information and Communications, pp. 1-6.
[60] Z. Wang, Y. Han, T. Lin, H. Tang and S. Ci,“Virtual network embedding by exploiting topology information,” in Global Communications Conference (GLOBECOM), 2012 IEEE, pp. 2603-2608.
[61] H. Cui, F. Kong and Y. Liu,“A new algorithm of virtual network embedding based on minimum node stress and adjacent principle,” in Global Communications Conference (GLOBECOM) Workshops, 2012 IEEE, pp. 792-796.
[62] H. Cui, W. Gao, J. Liu and Y. Liu,“A virtual network embedding algorithm based on virtual topology connection feature,” in 2013 16th International Symposium on Wireless Personal Multimedia Communications (WPMC), pp. 1-5.
[63] L. Gong, Y. Wen, Z. Zhu and T. Lee,“Toward profit-seeking virtual network embedding algorithm via global resource capacity,” in IEEE INFOCOM 2014 IEEE Conference on Computer Communications, pp. 1-9.
[64] E. Guler, G. Luo, K. Koneru and X. Gao,“Closeness-centrality based multicast-aware virtual network embedding,” in Global Communications Conference (GLOBECOM), 2016 IEEE, pp. 1-6.
[65] S. Zhang, Z. Qian, J. Wu and S. Lu,“An opportunistic resource sharing and topology-aware mapping framework for virtual networks,” in Proc. IEEE INFOCOM, 2012, pp. 2408-2416.
[66] S. Zhang, J. Wu and S. Lu,“Virtual network embedding with substrate support for parallelization,” in Global Communications Conference (GLOBECOM), 2012 IEEE, pp. 2615-2620.
[67] S. Zhang, Z. Qian, J. Wu, S. Lu and L. Epstein,“Virtual network embedding with opportunistic resource sharing,” IEEE Trans. Parallel Distrib. Syst., vol. 25, no. 3, pp. 816-827, Mar. 2014.
[68] H. Cao and L. Yang,“Topology attribute and global resource-driven virtual network embedding algorithm via novel node-ranking approach,” in2017 International Conference on Wireless Communications and Signal Processing (WCSP), pp. 1-7.
[69] H. Cao, Y. Zhu, L. Yang and G. Zheng,“A efficient mapping algorithm with novel node-ranking approach for embedding virtual networks,” IEEE Access, vol. 5, no. 1, pp. 22054-22066, 2017.
[70] L. Yin, Z. Chen, L. Qiu and Y. Wen,“Interference based virtual network embedding,” in2016 IEEE Conference on Communications (ICC), pp. 1-6.
[71] P. Zhang, H. Yao and Y. Liu,“Virtual network embedding based on computing, network and storage resource constraints,” IEEE IoT Journal, vol. 5, no. 5, pp. 3298-3304, 2018.
[72] S. Haeri and L. Trakjovic,“Virtual network embedding via monte carlo tree search,” IEEE Trans. Cyber., vol. 48, no. 2, pp. 510-521, 2018.
[73] H. Cao, L. Yang and H. Zhu,“Embedding virtual networks using a novel node-ranking approach via exploiting topology attributes and global network resources,” in2017 International Conference on Wireless Communications and Signal Processing (WCSP), pp. 1-6.
[74] Z. Xu, W. Liang and Q. Xia,“Efficient embedding of virtual networks to distributed clouds via exploring periodic resource demands,” IEEE Trans. Cloud Comp.,vol. 99, no. 1-1, 2016.
[75] F. Bianchi and F. L. Presti,“A markov reward nased greedy heuristic for the virtual network embedding problem,”2016 IEEE 24^{th} International Symposium on Modeling, Analisis and Simulation of Computer and Telecommunications Systems, pp. 373-378.
[76] L. D. Nguyen, N. Kim, S. Kim and C. Kim,“RT-VNE: A real-time strategy for virtual network embedding towards resource efficiency,”2017 International Conference on Information Networking, pp. 185-190.
[77] H. Cao, Y. Guo, Y. Li, H. Zhu and L. Yang,“NLTA: Node and link topological attributes based virtual network embedding,” in2018 IEEE Conference on Communications (ICC) Workshops, pp. 1-6.
[78] M. Chowdhury, M. Rahman,R. Boutaba,“Vineyard: Virtual network embedding algorithms with coordinated node and link mapping,” IEEE/ACM Trans. Netw., vol. 20, no. 1, pp. 206-219, Feb. 2012.
[79] M. Chowdhury, M. Rahman,R. Boutaba,“Virtual network embedding with coordinated node and link mapping,” in Proc. IEEE INFOCOM, Apr. 2009, pp. 783-791.
[80] M. Melo, S. Sargento, U. Killat, A. Timm-Giel and J. Carapinha,“Optimal virtual network embedding: node-link formulation,”IEEE Trans. Netw. and Serv. Manag., vol. 10, no. 4, pp. 356-368, Dec. 2013.
[81] R. Mijumbiet al.,“A Path Generation Approach to Embedding of Virtual Networks,”IEEE Trans. Netw. and Serv. Manag., vol. 12, no. 3, pp. 334-348, Sep. 2015.
[82] Q. Hu, Y. Wang,X. Cao,“Resolve the virtual network embedding problem: A column generation approach,” in Proc. IEEE INFOCOM, Apr. 2013, pp. 410-414.
[83] A. Jarray and A. Karmouch,“Decomposition approaches for virtual network embedding with one-shot node and link mapping,”IEEE/ACM Trans. Netw., vol. 23, no. 3, pp. 1012-1025, Jun.2015.
[84] H. Cao, Y. Zhu, G. Zheng and L. Yang,“A novel optimal mapping algorithm with less computational complexity for virtual network embedding,” IEEE Trans. Netw. and Serv. Manag., vol. 15, no. 1, pp. 356-371, 2018.
[85] H. Cao, L. Yang, J. Chen,“An exact VNE algorithm on optimization theory,” in Proc. 2016 IEEE International Conference on Consumer Electronics-Asia (ICCE-Asia), pp. 1-4.
[86] H. Cao, L. Yang, Y. Hu and J. Chen,“An exact VNE algorithm on integer linear programming,” in Proc. 2016 15^{th} International Conference on Optical Communications and Networks (ICOCN), pp. 1-3.
[87] I. Houdi and D. Zeghlache,“Exact adaptive virtual network embedding in cloud environments,” in2013 Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises, pp. 319-323.
[88] L. Nonde, T. Elgorashi and J. Elmirgahni,“Cloud virtual network embedding: Profit, power and acceptance,” in Global Communications Conference (GLOBECOM), 2015 IEEE, pp. 1-6.
[89] H. Cao, J. Chen and L. Yang,“Virtual network embedding based on restrictive selection and optimization theory,” in Proc. 2017 16^{th} International Conference on Optical Communications and Networks (ICOCN), pp. 1-3.
[90] H. Cao, Z. Qu, Y. Xue and L. Yang,“Efficient virtual network embedding algorithm based on restrictive selection and optimization theory approach,” China Commun., vol. 14, no. 10, pp. 39-60, Oct. 2017.
[91] S. Abdelwahab, B. Hamdaoui and M. Guizani,“BIRD-VNE: Backtrack-avoidance virtual network embedding in polynomial time,” in Global Communications Conference (GLOBECOM), 2014 IEEE, pp. 4983-4989.
[92] S. Abdelwahab, B. Hamdaoui and M. Guizani,“Efficient virtual network embedding with backtrack avoidance for dynamic wireless networks,” IEEE Trans. Wire. Commun., vol. 15, no. 4, pp. 2669-2683, Apr. 2016.
[93] J. Lischka and H. Karl,“A virtual network mapping algorithm based on subgraph isomorphism detection,” inProc. 1^{st} ACM Workshop VISA, 2009, pp. 81-88.
[94] L. Gong, H. Jiang, Y. Wang and Z. Zhu,“Novel location-constrained virtual network embedding (LC-VNE) algorithms towards integrated node and link mapping,”IEEE/ACM Trans. Netw., vol. 24, no. 6, pp. 3648-3661, 2016.
[95] L. Wang, H. Qu, J. Zhao and Y.Guo,“Virtual network embedding with discrete particle swarm optimisation,” Electronics Letters, vol. 50. No. 4, pp. 285-286, 2014.
[96] S. Qing, J. Liao, J. Wang, X. Zhu and Q. Qi,“Hybrid birtual network embedding with K-core decomposition and time-oriented priority,” in2012 IEEE Conference on Communications (ICC), pp. 2695-2699.
[97] X. Liu, Z. Zhang, X. Li and S. Su,“Optimal virtual network embedding based artificial bee colony,” J. Wireless Com. Network, Dec. 2016.
[98] T. Ghazar and N. Samaan,“A hierarchical approach for efficient virtual network embedding based on exact subgraph matching,” in Global Communications Conference (GLOBECOM), 2011 IEEE, pp. 1-6.
[99] S. Qing, Q. Qi, J. Wang, T. Xu and J. Liao,“Topology-aware virtual network embedding through Bayesian network analysis,” in Global Communications Conference (GLOBECOM), 2012 IEEE, pp. 2621-2627.
[100] X. Wang, M. Song, D. Yuan and X. Liu,“Robust virtual network embedding based on component connectivity in large-scale network,” China Commun., vol. 14, no. 10, pp. 164-179, Oct. 2017.
[101] S. Araujo, D. Guidoni and F. Souza,“A metaheuristic approach for the virtual network embedding problem,”2015 IEEE 14^{th} International Symposium on Network Computing and Applications, pp. 68-75.
[102] Z. Wang, J. Wu, G. Cheng and Y. Jiang,“Mutine: A mutable virtual network embedding with game-theoretic stochastic routing,” in Global Communications Conference (GLOBECOM), 2015 IEEE, pp. 1-6.
[103] X. Li, H. Lu, W. Zhou and P. Hong,“VNE-RFD: Virtual network embedding with resource fragmentation consideration,” in Global Communications Conference (GLOBECOM), 2014 IEEE, pp. 1841-1847.
[104] H. Zheng, J. Li, Y. Gong, W. Chen, Z. Yu, Z. Zhan and Y. Lin,“Link mapping-oriented ant colony system for virtual network embedding,”2017 IEEE Congress on Evolutionary Computation (CEC), pp. 1223-1230.
[105] M. R.Rahman and Raouf Boutaba,“SVNE: Survivable Virtual Network Embedding Algorithms for Network Virtualization,” IEEE Trans. Netw. and Serv. Manag., vol. 10, no. 2, pp. 105-118, Jun. 2013.
[106] M. Rahman, I. Aib,R. Boutaba,“Survivable virtual network embedding,” in Proc.2010 IFIP Netw., pp. 40-52.
[107] M. Khan, N. Shahriar, R. Ahmed,R. Boutaba,“Multi-path link embedding for survivability in virtual networks,” IEEE Trans. Netw. and Serv. Manag., vol. 13, no. 2, pp. 253-266, Jun. 2016.
[108] M. Khan, N. Shahriar, R. Ahmed,R. Boutaba,“SiMPLE: survivability in multi-path link embedding,” in Proc. IEEE 11^{th} Int. Conf. Netw. Service Manag., Barcelona, Spain, 2015, pp. 210-218.
[109] P. Gil, N. Jain,N. Nagappan,“Undersatnding network failures in data centers: Measurement, analysis, and implications,” ACM SIGCOMM Comput. Commun. Rev., vol. 41, no. 4, pp. 350-361, Aug. 2011.
[110] A. Markopoulou, G. Iannaccone, S. Bhattachryya, C. Chuah,C. Diot,“Characterization of failures in an IP backbone,” in Proc. IEEE INFOCOM, vol. 4, Hong Kong, Mar. 2004, pp. 2307-2317.
[111] A. Todimala and B. Ramamurthy,“A scalable approach for survivable virtual network topology routing in optical WDM networks,” IEEE J. Sel. Areas Commun., vol. 25, no. 6, pp. 63069, Aug. 2007.
[112] H. Jiang, L. Gong, Z. Zhu,“Efficient joint approaches for location-constrained survivable virtual network embedding,” in Proc. Global Communications Conference (GLOBECOM), 2014 IEEE, pp. 1810-1815, 2014.
[113] A. Xiao, Y. Wang, L. Meng, X. Qiu and W. Li,“Topology-aware virtual network embedding to survive multiple node failures,” in Proc. Global Communications Conference (GLOBECOM), 2014 IEEE, pp. 1823-1829, 2014.
[114] W. L. Yeow, C. Westphal,U. C. Kozat,“Designing and embedding reliable virtual infrastructures,” in Proc. ACM SIGCOMM Workshop on Virtualized Infrastructure Systems and Architectures (VISA’10), New Delhi, India, 2010.
[115] H. Yu, V. Anand, and Ch. Qiao,“Cost efficient design of survivable virtual infrastructure to recover from facility node failures,” in Proc. IEEE ICC 2011, pp. 1-6, 2011.
[116] C. Qiao, B. Guo, S. Huang, J. Wang, T. Wang,W. Gu,“A novel two-step approach to surviving facility failures,” inOFC/NFOEC 2011, pp. 1-3, Mar. 2011.
[117] Q. Hu, Y. Wang,X. Cao,“Location-constrained survivable network virtualiztion,” inProc. 35^{th} SARNOFF 2012, pp. 1-5, May, 2012.
[118] T. Guo, N. Wang, K. Moessner and R. Tafazolli,“Shared backup network provision for virtual network embedding,” in Proc.2011 ICC, pp. 1-5.
[119] S. Chowdhury, R. Ahmed, M. Khan, N. Shahriar, R. Boutaba, J. Mitra and F. Zeng,“Dedicated Protection for Survivable Virtual Network Embedding,” IEEE Trans. Netw. and Serv. Manag., vol. 13, no. 4, pp. 913-926, Dec. 2016.
[120] N. Shahriar, R. Ahmed, S. Chowdhury, A. Khan and R. Boutaba,“Generalized recovery from node failure in virtual network embedding,” IEEE Trans. Netw. and Serv. Manag., vol. 14, no. 2, pp. 261-274, Jun. 2017.
[121] S. Ayoubi, Y. Chen and C, Assi,“Towards promoting backup-sharing in survivable virtual network design,” IEEE/ACM Trans. Netw., vol. 24, no. 5, pp. 3218-3231, Oct. 2016.
[122] O. Soualah, N. Aitsaadi and I. Fajjari,“A novel reactive survivable virtual network embedding scheme based on game theory,” IEEE Trans. Netw. and Serv. Manag., vol. 14, no. 3, pp. 569-585, Sept. 2017.
[123] I. Houidi, W. Louati,D. Zeghlache,“A distributed virtual network mapping algorithm,” in Proc. IEEE International Conference on Communications (ICC’08), Beijing, China, 2008.
[124] I. Houidi, W. Louati, W. B. Ameur,D. Zeghlache,“Virtual network provisioning across multiple domains,” Computer Networks, vol. 55, no. 4, pp. 1011-1023, 2011, special Issue on Architectures and Protocols for the Future Internet.
[125] M. Chowdhury, F. Sauel,R. Bouta,“Polyvine: policy-based virtual network embedding across multiple domains,” in Proc. of the second ACM SIGCOMM workshop on Virtualized infrastructure systems and architectures, ser. VISA’10, New York, NY, USA,: ACM, 2010, pp. 49-56.
[126] D. Dietrich, A. Rizk,P. Papadimitriou,“Multi-provider virtual network embedding with limited information disclosure,” IEEE Trans. Netw. and Serv. Manag., vol. 12, no. 2, pp. 188-201, May. 2015.
[127] T. Mano, T. Inoue, D. Ikarashi, K. Hamada, K. Mizutani,O. Akashi,“Efficient virtual network optimization across multiple domains without revealing private information,” IEEE Trans. Netw. and Serv. Manag., vol. 13, no. 3, pp. 477-488, Jun. 2016.
[128] T. Mano, K. Mizutani,O. Akashi,“Secure resource provisioning across multiple domains,” in Proc. IFIP/IEEE IM, Ghent, Belgium, 2013, pp. 1129-1134.
[129] J. Brickell and V. Shmatikov,“Privacy-preserving graph algorithms in semi-honest model,” in Proc. ASIACRYPT, Chennai, India, 2005, pp. 236-252.
[130] M. Fukeshima, K. Sugiyama, T. Hasegawa,A. Nakao,“Minimum disclosure routing for network virtualization and its experimental evaluation,” IEEE/ACM Trans. Netw., vol. 21, no. 6, pp. 1839-1851, Dec. 2013.
[131] S. Machiraju and R. H. Katz,“Verifying global invariants in multip-rovider distributed systems,” in Proc. ACM HotNets, San Diego, CA, USA, 2004, pp. 149-154.
[132] M. Burkhart, M. Strasser, D. Many,X. Dimitropoulos,“SEPIA: Privacy-preserving aggregation of multi-domain network events and statistics,” in Proc. USENIX Security, Washington, DC, USA, 2010, p. 15.
[133] A. Leivadeas, C. Papagianni,S. Papavassiliou,“Efficient resource mapping framework over networked clouds via iterated local search-based request partitioning,” IEEE Trans. Parallel Distrib. Syst., vol. 24, no. 6, pp. 1077-1086, Jun. 2013.
[134] F. Esposito, D. Paola,I. Matta,“A general distributed approach to slice embedding with guarantees,” in Proc. IFIP Netw., New York, NY, USA, May 2013, pp. 1-9.
[135] J. Duan, Z. Guo and Y. Yang,“Cost efficient and performance guaranteed virtual network embedding in multicast fat-tree DCNs,” in Computer Communications (INFOCOM), 2015 IEEE Conference on, May. 2015, pp. 136 - 144.
[136] K. Guo, Y. Wang, X. Qiu, W. Li, A. Xiao,“Particle Swarm Optimization Based Multi-Domain Virtual Network Embedding,” in Integrated Network Management (IM), 2015 IFIP/IEEE International Symposium on, May. 2015, pp. 798 - 801.
[137] S. Gong, J. Chen, X. Yin and Q. Zhu,“Survivable virtual network embedding across multiple domains,”2016 2^{nd} IEEE International Conference on Computer and Communications, pp. 2391-2396.
[138] S. Su, Z. Zhang, X. Cheng, Y. Wang, Y. Luo and J. Wang,“Energy-aware virtual network embedding through consolidation,” inProc. IEEE INFOCOM WS-CCSES: Green Networking and Smart Grids, 2012, pp. 2708-2713.
[139] S. Su, Z. Zhang, A. Liu, X. Cheng, Y. Wang and X. Chao,“Energy-aware virtual network embedding,” IEEE/ACM Trans. Netw., vol. 22, no. 5, pp. 1607-1620, Oct. 2014.
[140] Z. Zhang, S. Su, X. Niu, J. Ma, X. Cheng and K. Shuang,“Minimizing electricity cost in geographical virtual network embedding,” in Global Communications Conference (GLOBECOM), 2012 IEEE, pp. 2609-2614.
[141] Z. Zhang, S. Su, J. Zhang, K. Shuang and P. Xu,“Energy aware virtual network embedding with dynamic demands,” in2015 IEEE Conference on Communications (ICC), pp. 5386-5391.
[142] Z. Zhang, S. Su, J. Zhang, K. Shuang and P. Xu,“Energy aware virtual network embedding with dynamic demands: Online and offline,” Computer Networks, vol. 93, no. 3, pp. 448-458, Dec. 2015.
[143] J. Botero, X. Hesselbach, M. Duelli, D. Schlosser, A. Fischer and H. Meer,“Energy efficient virtual network embedding,” IEEE Commun. Lett., vol. 16, no. 5, pp. 756-759, May 2012.
[144] X. Chen, C. Li and Y. Jiang,“Optimization model and algorithm for energy efficient virtual node embedding,” IEEE Commun. Lett., vol. 19, no. 8, pp. 1327-1330, Aug. 2015.
[145] L. Nonde, T. Gorashi and J. Elmirghani,“Energy efficient virtual network embedding for cloud networks,” Journal of Lightwave Technology, vol. 33, no. 9, pp.1828-1849, May. 2015.
[146] S. Gong, J. Chen, X. Yin and Q. Zhu,“Energy-efficient virtual network embedding for heterogeneous networks,”2016 First IEEE Internation Conference on Computer Communication and the Internet, pp. 85-90.
[147] L. Nonde, T. Elgorashi and J. Elmirgahni,“Virtual network embedding employing renewable energy sources,” in Global Communications Conference (GLOBECOM), 2016 IEEE, pp. 1-6.
[148] S. Jia, G. Jiang, P. He and J. Wu,“Efficient algorithm for energy-aware virtual network embedding,” Tsinghua Science and Technology, vol. 21, no. 4, pp. 407-414, Aug. 2016.
[149] P. Han, L. Guo, Y. Liu, X. Wei, J. Hou and X. Han,“A new virtual network embedding framework based on QoS satisfaction and network reconfiguration for fiver-wireless access network,” in2016 IEEE Conference on Communications (ICC), pp. 1-7.
[150] G. Chchlidakis and V. Friderkos,"Low latency virtual network embedding for mobile networks,"in 2016 IEEE Conference on Communications (ICC), pp. 1-6.
[151] G. Chchlidakis and V. Friderkos,“Mobility aware virtual network embedding,” in 2015 IEEE Conference on Communications (ICC), pp. 1-6.
[152] G. Chchlidakis and V. Friderkos,“Mobility aware virtual network embedding,” IEEE Trans. Mob. Comp., vol. 16, no. 5, pp. 1343-1356, May 2017.
[153] P. Lv, Z. Cai, J. Xu and M. Xu,“Multicast service-oriented virtual network embedding in wireless mesh networks,” IEEE Commun. Lett., vol. 16, no. 3, pp. 375-377, Mar. 2012.
[154] W. Hou, Z. Ning, L. Guo, Z. Chen and M. Obaidat,“Novel framework of risk-aware virtual network embedding in optical data center networks,” IEEE System Journal, vol. 99, no. pp, pp. 1-1, 2017.
[155] J. Wu, X. Xie, Y. W and G. Chen,“Lower bounds and a nearly fastest general parallel branch-and-bound algorithm,” Journal of Sys. Engi. Elert., vol. 11, no. 3, pp. 65-73, Mar. 2000.
[156] A. I. Cohen and M. Yoshimura,“A branch-and-bound algorithm for unit commitment,” IEEE Power Engi. Review, vol. Per-3, no. 2, Feb. 1983.
[157] M. F. Bari, R. Boutaba, R. Esteves, L. Z. Granville, M. Podlesny, M. G. Rabbani, Q. Zhang and M. Zhani,“Data center network virtualization: A survey,” IEEE Commun. Sur.& Tuto., vol. 15, no.2, pp. 909-928, 2013.
[158] R. Mijumbi, J. Serrat, J. Gorricho, N. Boutern, F. D. Turck and R. Boutaba,“Network function virtualization: State-of-the-art and research challenges,” IEEE Commun. Sur.& Tuto., vol. 18, no.1, pp. 236-262, 2016.
[159] A. Lombardo, G. Morabito and G. Schembra,“A novel framework compounding statistical traffic modeling and aggregate-level service curve disiplines: network performance and efficiency implications,” IEEE/ACM Trans. Netw., vol. 12, no. 3, pp. 443-455, Jun. 2004.
[160] R. Bolla, R. Bruschi, F. Davoli and C. Lombardo,“Fine-grained energy-efficient consolidation in SDN networks and devices,” IEEE Trans. Netw. and Serv. Manag., vol. 12, no. 2, pp. 132-145, Jun. 2015.
[161] S. Ma, N. E. Jerger, Z. Wang, M. Lai and L. Huang,“Holistic routing algorithm design to support workload consolidation in NoCs,” IEEE Trans. Com., vol, 63, no. 3, pp. 529-542, Mar. 2014.
[162] D. He, R. Ye, A. Chan, M. Guizani and Y. Xu,“Privacy in the internet of things for smart healthcare,” IEEE Commun. Maga., vol. 56, no. 4, pp. 38-44, Apr. 2018.
[163] F. Toledo, E. Sauma and S. Jerardino,“Energy cost distortion due to ignoring natural gas network limitations in the scheduling of hydrothermal power systems,” IEEE Trans Pow. Sys., vol. 31, no. 5, pp. 3785-3793, May 2016.
[164] M. Nick, R. Cherkaoui, M. Paolone,“Optimal planning of distributed energy storage systems in active distribution networks embedding grid reconfiguration,” IEEE Trans Pow. Sys., vol. 33, no. 2, pp. 1577-1590, Feb. 2018.
[165] H. Cao, Y. Guo, Z. Qu, S. Wu, H. Zhu and L. Yang,“ER-VNE: A Joint Energy and Revenue Embedding Algorithm for Embedding Virtual Networks” IEEE Access, vol. 6, no. 1, pp. 47815-47827.
[166] J. T. Taylor and J. K. Omura,“Spread spectrum technology: a solution to the personal communications services frequency allocation dilemma,” IEEE Commun. Mag., vol. 29, no. 2, pp. 48-51, Feb. 1991.
[167] M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka and A. Hirano,“Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138-145, Aug. 2010.
[168] C. Liang, and F. Yu,“Wireless network virtualization: a survey, some research issues and challenges,” IEEE Commun. Sur.& Tuto., vol. 17, no.1, pp. 358-380, 2015.
[169] L. Qian, Y. Wu, H. Zhou and X. Shen,“Non-orthogonal multiple access vehicular small cell networks: Architecture and solution,” IEEE Network, vol. 31, no. 4, pp. 15-21, Apr. 2017.
[170] Q. Zhou, C. Wang, S. McLaughlin and X. Zhou,“Network virtualization and resource description in software-defined wireless networks,” IEEE Commun. Maga., vol. 53, no. 11, pp. 110-117, Nov. 2015.
[171] J. S. Zander, C. Mayer, B. Ciobotaru, R. Lisicki, S. Schmid and A. Feldmann,“Unified programmability of virtualized network functions and software-defined wireless networks,” IEEE Trans. Netw. and Serv. Manag., vol. 14, no. 4, pp. 1046-1060, Dec. 2017.
[172] T. Mano, T. Inoue, K. Mizutani and O. Akashi,“Reducing dense virtual networks for fast embedding,” in 2016 IEEE INFOCOM, pp. 1-9.
[173] L. Zhou, D.Wu, Z. Dong and X. Li,“When collaboration hugs intelligence: Content delivery over ultra-dense networks,” IEEE Commun. Maga., vol. 55, no. 12, pp. 91-95, Dec. 2017.
[174] G. Koudouridis and P. Soldati,“Spectrum and network density management in 5G ultra-dense networks,” IEEE Wire. Commun., vol. 24, no. 5, pp. 30-37, May 2017.
[175] J. Li, F. R. Yu, G. Deng, C. Luo, Z. Ming and Q. Yan,“Industrial internet: A survey on the enabling technologies, applications and challenges,” IEEE Commun. Sur.& Tuto., vol. 19, no.3, pp. 1504-1526, 2017.
[176] S. Chen, F. Qin, B. Hu, X. Li and Z. Chen,“User-centric ultra-dense networks for 5G: Challenges, methodologies, and directions,” IEEE Wire. Commun., vol. 23, no. 2, pp. 78-85, Feb. 2016.
[177] Y. Ni, G. Huang, S. Wu, C. Li, P. Zhang and H. Yao,“A PSO based multi-domain virtual network approach,” China Commun., vol. 16, no. 4, pp. 105-119, Apr. 2019.
[178] M. Lu, Y. Lian, Y. Chen and M. Li,“Collaborative dynamic virtual network embedding algorithm based on resource importance measures,” IEEE Access, vol. 6, pp. 55026-55042, 2018.
[179] C. A. Fuster, M. Zangiabady, J. Lara and J. R. Loyola,“Online virtual network embedding based on virtual links’ rate requirements,” IEEE Trans. Netw. and Serv. Manag., vol. 15, no. 4, pp. 1630-1644, Dec. 2018.
[180] H. Cao, S. Wu, H. Zhu and L. Yang,“An efficient embedding algorithm for energy multi-domain virtual network embedding,” in 2018 IEEE Global Communications Conference (GLOBECOM) Workshops, pp. 1-7.