When “and” connects two 'subjects', can we remove the article pertaining to the second 'subject'?

Solution 1:

Instead of removing the before GPU in the sentence

The implementation of the algorithms on the CPU and the GPU is presented.

why not use the much clearer wording from your explanatory sentence below the revised wording:

The algorithms are implemented both on the GPU and on the CPU.

I find the wording "The implementation of X is presented" almost completely opaque, whereas I have no trouble at all imagining that I understand what "The algorithms are implemented" means.

As a matter of comprehensibility to readers or hearers—not as a matter of grammatical defensibility—I recommend that you take into account the complexity and abstractness of your sentence before you start "simplifying" it by removing elements that may help make parallel structures or other aspects of the sentence's internal logic easier to recognize.