Q:

comma after 'To this end'?

I have the following sentence:
"To this end(,) efficient algorithms are necessary". Is the comma correct or not?
I'd appreciate every comment and would be thankful for your help.

A:

When deciding to use a comma, it's often useful to imagine saying the phrase, and whether it would work better with a slight pause at that point.  The comma is like the written equivalent of the pause.
In this case, the pause in speaking aids comprehension for the listener, and so the comma aids comprehension for the reader.  From a grammatical point of view, it breaks up the sentence into phrases - a coding equivalent would be the use of round braces to say "this stuff goes together".

