Can you please provide some details about Melzak algorithm for four point steiner tree problem?

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Firoz Ahmad

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.56.4182&rep=rep1&type=pdf

http://www.math.ucsd.edu/~ronspubs/14_02_Steiner.pdf

https://people.mpi-sws.org/~dreyer/papers/steiner/steiner.pdf

https://arxiv.org/pdf/1605.01172.pdf

Md Arafat Habib

This PHD thesis might help....

Fabrice Clerot

http://www.maths.dur.ac.uk/Ug/projects/highlights/CM3/Soothill_Steiner_report.pdf

section 5.2.2 has a gentle step by step illustrated explanation of the algorithm for 4 points