 Sep 2018

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numbers
"points"?

and its distance to all points on its left willincreasebyδ
This relies on an unstated fact that the shortest path between these points is along this line. I don't know how familiar you're expecting the reader to be with this.

the line
"points on a line"

But a highquality solution is not the same thing as a meaningful solution
Now we're talking

tor of 2 is NPhard, and is therefore as hard as solving the problemexactly
At this point I wonder: "How does one then distinguish among the many possible solutions that are 2approximations?"

space of partitionsΠ(X), we can search oversubsets ofXof sizek
Perhaps a note on how much smaller the latter is?

Effectively, we are searching for a partition in which the maximum radiusof a cluster is minimized.
It's been a few pages since jumping into definitions. It may be worthwhile to emphasize somewhere earlier that these particular definitions are not applicable to every clustering problem, but rather it's a set of examples that cover a large set of techniques while showing many of the important considerations.

help guide how we think about clustering a data set
Now I'm hooked

“related”.
Should these quotes be `` (double backtick) '' (double apostraphe)?

collection
"collections"
