It is well known that k-means algorithm suffers in the presence of outliers. k-means++ is one effective method for cluster center initalization. I was going through the PPT by the founders of the method, Sergei Vassilvitskii and David Arthur http://theory.stanford.edu/~sergei/slides/BATS-Means.pdf (slide 28) which shows that the cluster center initialization is not affected by outlier as seen below.
As per the k-means++ method, the farthermost points are more likely to be the initial centers. In this way the outlier point (the rightmost point) must also be an initial cluster centroid. What is the explanation for the figure?