Best way to fusion two list of clusters
You could create an undirected graph which nodes are the clusters from A and B, two clusters being connected if they have a common dot. This graph can be built in time $O(n)$ where $n$ is the number of dots. Then the problem is to find the connected components of this graph. It is a standard problem that has a solution in linear time in terms of the number of edges and vertices of the graph. The clusters from each connected components are then fusioned to create the resulting clusters.