"This means that you get the speed of a deferred renderer (render time = light count + mesh count) with a drastically reduced memory footprint."

The speed of a deferred renderer has nothing to do with your algorithm at all. The speed in deferred comes in the fact that you run the pixel shader once for every pixel on the screen. You make pixel shader overdraw = 0. In your algorithm you would still draw an object with a pixel shader and then another object can come along and redraw over that pixel and have to run a pixel shader again (2x for the same pixel).

The algorithm itself doesnt make much sense to me. Why is it a cube map again? What does a mesh use to find the correct light in the cubemap? Why wouldnt it just be a 2D texture of the lights? How exactly does the light get mapped into the cubemap?(its not a 3d Array, its simply 6 faces that designate up down left righ bottom top.

Yes, you don't have the experience enough to finalize your algorithm. I'm planning to do something similar to this, however you have some holes to get to the end and you are in no way related to deferred rendering by this approach.

Ideas are just that. Consider throwing together a prototype/proof of concept that actually shows the lighting method and relevant shaders, and perhaps allows for some preliminary verification and performance testing. Also consider looking into tiled forward rendering, as I think that's where things are headed in the future.

In this, the pixel shader would be run once for every light to store it in the cube maps

Generally, a cubemap represents the scene from a certain view point. For instance, they can be used to render the scene around a point and used to draw rough environment reflections on objects. "rough" because it will only be accurate from one specific position in the scene. Of course it works well for things like a skybox (which is "infinitely" far away and looks the same from every point in the scene).

So... what exactly are you putting in your cubemap? Is the end result that there will be a single texel somewhere in the cubemap for each light?

you could find out how to color each fragment by getting a vector from the camera's position towards the mesh, reflect that vector off the mesh, and finally find which light that reflection vector is pointing at in the cube maps.

What are the chances that that reflection vector will line up exactly with the texel that contains the light information? Pretty small. Or does your cubemap contain large areas that cover a light's influence? If so, how would you handle overlapping lights?

(also, reflecting the eye vector off the mesh will help you calculate the specular component, what about diffuse?)

Maybe I'm just not understanding your description, but I still don't see how your algorithm makes any sense. As Promit suggested, try coming up with a proof of concept. I think it will quickly become obvious where things fall apart.

I'm not going to go into much depth here, but almost everything you have said really shows your inexperience. Based on that, I would just say don't plan on doing this. You can make games look good with forward rendering, deferred whatever. Don't try to implement the greatest lighting model when you aren't fully grasping things. Really quickly:

"then once more for every mesh when rendering to a final output buffer; just like a deferred renderer."Overdraw can occur regardless of what rendering method is used"
Uh....deferred rendering has 0 pixel shader overdraw. The initial filling of the buffers of course will have some overdraw, but its not like its wasting time running crazy pixel shaders. All lighting shaders are run once for ever pixel. 0 pixel shader (lighting) overdraw.

"but it can be reduced if each object is sorted in the scene based on its position from the camera (but I'm not really worried about it at the moment)."
Yes. In a deferred renderer you would be doing this as well to reduce the G-Buffer initial pass overdraw, but not the lighting pass overdraw.

"Think of having a skybox but with a bunch of lights' colors and positions only."
So I have a 3d light: A and B. A = vec3(-100,10,0) B = vec3(-110,10,0). Where would these be rendered into the cube map? If you use simply their position as a vector to render to the cube map....they render to the same spot. A cube map is 6 2D textures, it is not a 3d array. A 3D array would be a cube map with slices cut through it. and even then an actual 3d Texture wouldnt work for your algorithm. Not going to explain to you why because I don't think you will get it.


"Then, as I noted earlier, you could find out how to color each fragment by getting a vector from the camera's position towards the mesh, reflect that vector off the mesh, and"
This wont work. If you are actually rendering the cube map lights as actual spherical geometry... then what you have essentially is cube mapping/environment mapping. But you would have to render all the lights each frame for each mesh. So much wrong with this algorithm.
And if you are talking about rendering geometry, what happens when 2 lights geometry overlap in the cube map?

"What are the chances that that reflection vector will line up exactly with the texel that contains the light information? Pretty small. Or does your cubemap contain large areas that cover a light's influence? If so, how would you handle overlapping lights?"

Same thing I said pretty much. If you are only rendering to 1 pixel your light information, then it is still wrong. Noither approaches will work.