It guarantees the maximum volume size of selected points with minimum number of points (Figure 2 (c)).
it does not reduce a redundancy between the points over the convex-hull, and usually choose larger number of sentences than k. Marcu (1999) shows an interesting study regarding an importance of sentences: given a document, if one deletes the least central sentence from the source text, then at some point the similarity with the reference text rapidly drops at sudden called the waterfall phenomena.