You are spot on on the paper that I referenced. As you can see in 4.3 which is in page 3, the paper mentioned two algorithms for sentence selection. These are Summation-Based Selection and Density-Based Selection. Which is SBS and DBS respectively.
Summarizing only blogs posts seems a bit limiting to me. (Btw, I'm not trying to be negative, congrats on your success! texteaser looks great!)
I implemented a custom version (mainly changed the scoring scheme to include TF/IDF of words for initialized scoring) of TextRank and loved it.
The main thing I liked about it was how general it was. Words are nodes and sentences are vertices. Then you basically use pagerank to rank the sentences according the graph representation.
I'm a little bit familiar with TextRank because I stumbled upon it when I'm doing my research. I also read several algorithms but forgot what they are called.
News is the most broadly applicable use for this so leveraging that isn't a bad thing. There's always a trade off of broad applicability vs overfitting for a particular case to get better results.
Thanks for the insight! Again great work.