I've got a scan of a fictional star chart, but every single star has its fixed spot. 
Now, as a volunteer, I have to clean up that very map. I decided to use Inkscape for this, for many reasons.

I traced the bitmap scan, and obviously, I got a lot of somewhat roundish shapes. Alas, they aren't round enough. Some have even quite a weird shape. 
I tried the "simplify" tool, but that made things worse, if anything. 

Can anyone help me please? There's more than 3,000 stars in different sizes, so if I have to do this manually, I go nuts. 

Example 1 is how it's now (never mind the underlying bitmap, I can easily remove that one)
Example 2 is how it should be 
Example 3 is another portion of the star map. I cannot upload the entire thing due to copyright restrictions beyond my control. And I cannot find the part of the map where I got the screenshot, but I sincerely doubt that this would be relevant. 

There´s a LPE (path effect) for this:

Good grief! This works great! :D 
Not for everything, but still! Great! :D 

This is what I was looking for. Will save me a lot of time and work. 
Thanks a lot!!! 

One more thing, though. I have to group the shapes first, or I still have to do them one by one.
With 3,000+ objects, that's a no go, so yes, group and apply the effect. 

But... when I ungroup them afterwards, they fall back in their original shapes, so that's a bummer. Is there a solution to that too? 

As with all Path effects go Path->Objects to Path to burn in the circular shapes. Why do you say it don´t work for everything? It works on groups, can reconstruct circles from 2 nodes or 20 and more nodes straight lines into 4 nodes perfect circles with method: "Force circle" as I displayed.

It didn't work for everything, because there are overlapping circles in the original, that are considered to be 1 object after the tracing. When I force circle on those, they turn into 1 single circle, instead in overlapping circles. 
Or at least that's what I got. But doing those manually didn't take me THAT long. Finished this part of the project in about an hour, which is so much faster than drawing all of the circles manually.

Thanks a lot! :) 

Ok - didn´t think about overlapping objects to be honest - glad you got it sorted.