How to use 'pdist' for specified clustering technique for 2D dataset

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Hi there,
I have two-dimensional timeseries dataset and need to choose a subset using clustering method of Maximum Dissimilarity Algorithem(MDA) as in the attached figure.
Although I was trying to use 'pdist' for the application, I'm struggling to implement this method according to its description.
I need to know that, is it possible to implement this with 'pdist' or are there any other in-built functions to process this to save the computational time?
I would be greatful if someone can help me solve the issue using random datasets.
Thank you very much.
Please note that the figures are extracted from following journal paper.

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