I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-problem/4090360?noredirect=1#comment8537059_4090360.
There is a link gain between a server and a user. The farther away the user is, the lower the gain. Sometimes, there is zero gain is the distance between a user and server is too high. We do not want to put one user in a cluster where the user has zero gain for one of the servers belonging to user cluster.
I want to form the cluster such that the users have better overall gain. Also, we prefer that the servers are closer to each other to reduce the overall communication delay as the servers may need to communicate to each other.
The clustering constraints I have are as follows:
- There is a maximum cluster size limit.
- Minimum cluster size is one.
- The number of clusters is variable.
- Since there is individual cluster size limit, there exists a number that dictates the minimum number of clusters the system can have, which is number of servers/maximum cluster size.
The objective is to maximum the overall gain of the whole system, which is the sum of individual user gains.
User gain is decided by sum-gain from its own cluster servers divided by sum of the gains from the remaining servers in the system.