# Integrally or Comprehensively

I am looking for an adverb that implies "all at the same time" or ""in an all-inclusive way". My sentence is like this:

"The above algorithm comprehensively solves Sub-problems 1, 2, and 3 of the first optimization problem presented in the previous section"

I am wavering between integrally and comprehensively. Any better suggestion?

• The normal adverb for at the same time is simultaneously. In your example you explicitly list all the sub-problems, so "all" is to some extent redundant. But if you need to convey that aspect as well, you could always say This algorithm simultaneously and fully solves the problem [for all possible values of all variables]. And perhaps in a few years we'll be talking about algorithms that solve problems quantumly. Aug 9, 2015 at 11:50
• @FumbleFingers: I agree with you. However, I was looking for something with a positive connotation rather than neutral. The fact that the algorithm solves all the problems at same time is one of the contributions of the paper I am writing. Hence, I wanted to indirectly emphasis on this fact, without sounding too braggy! Guess I was expecting too much from a word, I will probably add the "and fully" as you suggested to get what I want. If you put it as an answer I will accept it. Thanks! Aug 10, 2015 at 9:47
• There are plenty of written instances of algorithm fully solves and algorithm simultaneously solves in Google Books. But I've no idea if the latter relates to the simultaneous equations I learned about at school, so I'm diffident about going beyond a comment here. I also note that there are no written instances of algorithm comprehensively solves, which suggests my concept of for all possible values of all variables may be misplaced. I'm half inclined to think the question might be better asked on Maths.SE. Aug 10, 2015 at 12:58

Use Simultaneously ...

"The above algorithm simultaneously solves Sub-problems 1, 2, and 3"

"compreshensively" would really be taken to mean "solves completely, once and for all" so would really be used for a single problem, or for a collection of problems, where any currently extant solution may be in doubt.

Uhm. Sort of drifted here by accident as I was surfing, so this won't exactly be an expert opinion, but. Couldn't you write "The above algorithm encompass a solution to sub-problems 1, 2 and 3 of the first optimization problem presented in the previous section"

I hope you'll find a word, or phrase, to your liking.

I'd say comprehensively.

Integrally means it's part of the whole. But the algorithm isn't part of the problem, the problems aren't part of the algorithm, and the problems aren't parts of one another either.

The algorithm is a different entity to the problems, so they're not integrated.

Perhaps exhaustively