How to convince your PhD adviser about the research value of the topic? I'm already in the second year of my PhD studies and my advisor insists on pursuing a very vague track, in order to produce some results that may be publishable. The problem is that the topic itself was extensively studied in the past two decades and there's little maneuver space without overlapping with others' past ideas (it's in applied Computer Science). My adviser seems to be constrained by his grant committee to have a solution for the topic's problem using a certain kind of technique that will be outperformed by other, more specific algorithms right from the start. Although it has other benefits, they're not interesting for this particular topic (since they're not going to be used in any way). 

To put it simple, how can you tell your advisor that what they want you to do is like killing flies with TNT and then have the denotation site rebuilt in order to get rid of those flies? (in an elegant way, of course).

I should mention that my advisor has a different area of expertise than the one chosen for my PhD program and often seems not to having the slightest hints on what state of the art means for that particular field and why it is important not to reiterate past methods and algorithms just because they can be applied in a slightly different field from the one they were initially proposed for.
I believe you are rushing ahead of yourself. In popular areas as applied CS, all areas one way or another may be considered overcrowded. Take any hot topic right now and you are going to see multiple publications with incremental updates / improvements. Still, a new dataset or a new test case ignites new research and so-on. No CS problem may be considered entirely solved. The fastest algorithm may be impossible to use for some datasets, its preprocessing may not scale and slower algorithms may be more parallelizable and more attractive to use. New hardware (CUDA / multiprocessor chips) change the way we write algorithms and so-on. There is a not a single criteria for what is the "best" solution. Stil, this is something you cannot know just by a literature survey.

Have you actually implemented any of the previous solutions to get a grasp of their advantages / disadvantages? Will you be able tomorrow to implement on your src code the state-of-the-art in this suggested problem or you assume it is too perfect to improve (to avoid the trouble of actually doing the implementation). Have you asked /contacted any of the authors if they can provide datasets or binaries for their solutions? Have you actually created multiple datasets to test previous solutions (and yours)? Or is everything just in your head. If yes, you must get them out of your head and into your PC. 

If you actually implemented a quick and dirty (1-2 months) implementation of your advisor's suggestion, get some insight of how it behaves and 100% confirmed that your results are much worse than state-of-the-art solutions then no one (including your advisor) will object to you changing direction (no one likes dead ends). But this time will not be wasted. You have learnt what went wrong, you improved your coding skills and you see the research area more clearly. Maybe then, you can even come up with a test-case where your solution is way better than previous works, you perhaps know how to combine this problem with other related sub-problems and you have a solution that works (although not optimally) to partially satisfy the grant's requirements.

So, out of the books / papers and start writing some code!! It is more fun after all.