It depends what you mean by "fast" here.

However, the first thing to notice is that in SDN the centralized controller is omniscient (which is why it is sometimes called a God-box). So, it has a full picture of what is going on in your network.

The network is represented as a graph with routers/switches as nodes and links between them as edges. You can weight the nodes according to maximum performance (in pps) and/or current/smoothed/predicted load and the links according to maximum data rate (bps) and/or current/smoothed/predicted loading.

Now the routing problem becomes a graph optimization problem for which we have excellent algorithms. Note that you can do optimizations that are not possible using distributed routing protocols (which can generally only handle objective functions and/or constraints that are additive or multiplicative in hops).

So what do you mean by "fast"? A fast algorithm (there are such). Fast online routing of a new service? That can take time as the SDN controller has to touch all the SDN switches along the path (an alternative is segment routing where only the ingress switch needs to be informed). Fast recovery from failures (rerouting)? That can be a problem as the controller is a single point of failure (and there is no way to completely escape this problem - see the CAP theorem).

Y(J)S

Dear Kumar Gopal,

"Routing in SDN" is a very important topic. I've attached my small list of literature sources. I would like to point out an important importance of IPv6 segment routing (SRv6) for SDN. Various programmable SD networks, for example such as SD-WANs, can be set up using SRv6 and NFV (Network Functions Virtualization) with SDN.

Best regards and much success

Anatol Badach

Sahrish Khan, Sadaf Tanvir, Nadeem Javaid: “Routing Techniques in Software Defined Networks: A Survey”; 13th IEEE International Bhurban Conference on Applied Sciences & Technology (IBCAST 2016), Jan 2016

https://www.researchgate.net/publication/301757741

Slavica Tomovic, Nedjeljko Lekic, Igor Radusinovic, Gordana Gardasevic: A new approach to dynamic routing in SDN networks; 18th Mediterranean Electrotechnical Conference (MELECON), Apr 2016; DOI: 10.1109/MELCON.2016.7495433

https://ieeexplore.ieee.org/document/7495433

Asad Mahmoud Alnaser: A METHOD OF MULTIPATH ROUTING IN SDN NETWORKS; Advances in Computer Science and Engineering, Vol 17(1), Jun 2018; DOI: 10.17654/CS017010011

https://www.researchgate.net/publication/326089884

Xiaolan Hou, Muqing Wu, Min Zhao: An Optimization Routing Algorithm Based on Segment Routing in Software-Defined Networks, Sensors (Basel), Vol 19(1), Jan 2019; DOI: 10.3390/s19010049

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6339048/

Wu Jiawei, Qiao Xiuquan, Nan Guoshun: Dynamic and adaptive multi-path routing algorithm based on software-defined network; International Journal of Distributed Sensor Networks, Vol 14(10), Sep 2018

https://journals.sagepub.com/doi/pdf/10.1177/1550147718805689

Erdal Akin, Turgay Korkmaz: Comparison of Routing Algorithms With Static and Dynamic Link Cost in Software Defined Networking (SDN), IEEE Access, Vol 7, Oct 2019

https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8864963

AI algorithm or intelligent routing are useful in these fields.