Making polygons "complete" in QGIS?

Question

I've done the following process:

1. take a set of points, each one representing a hotel with a field that says the "neighborhood" that the hotel is in (field is called "full_hierarchy")
2. Performed SNN clustering on these points
3. Created Voronoi Polygons using the clusters
4. Dissolved the Voronoi polygons on the field "full hierarchy")

And I get this:

My problem is that there are bits of each polygon inside of other polygons, as you can see in my image where I have highlighted one of my neighborhoods.

Any ideas how I can get rid of these bits so that each of my polygons is complete with no "islands" in them?

I am going to be doing this on a mass scale, so I need a process that I can do on QGIS

Would also be interested in smoothing the polygons, if possible.

EDIT: Using the options recommended to be below when using the eliminate sliver polygons:

But the output layer looks exactly the same - nothing changes?

Answer 1

As @Kazuhito suggested the 'Eliminate Sliver Polygons' is the tool to use in this scenario. The tricky part is determining your cutoff point for feature removal. You will want to calculate the area for all the features in the layer. Using the area calculated find the value at which you would classify a feature as an "island"(sliver). In the 'Eliminate Sliver Polygon' select your layer and put in the area field as the selection attribute. Then set the comparison the less than or equal to the value that you have decided to be corresponding to the largest "island". The merge option will be based on your preference for what will match your study requirements. I generally merge with the feature that has the largest common boundary as it tend to maintain the integrity of my analysis better than the other methods. After that you need only designate a filename and location and you are good to go.