Explanation of Equation for K-means Initialization

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I'm currently working on a college project and was having trouble deciphering a formula I ran across. The problem involves the initialization of cluster centers for the K-means algorithm, and here is how it is shown:

Consider the following heuristic method for selecting the initial cluster center positions:

  1. Choose 1st center c1 as point A
  2. For k=2,...,K set enter image description here, where X is the set of data points.

I understand that you have to measure the Euclidean distance between the points and the centers, but I'm confused by what the max(min (Euclid distance)) means.

Thanks you in advance!