High-density model of content distribution network

It is well known that optimal server placement is NP-hard. We present an approximate model of a content distribution network for the case when both clients and servers are dense, and propose a simple server allocation and placement algorithm based on high-rate quantization theory. The key idea is to regard the location of a request as a random variable with probability density that is proportional to the demand at that location, and the problem of server placement as source coding, i.e., to optimally map a source value (request location) to a codeword (server location) to minimize distortion (network cost). This view leads to a joint server allocation and placement algorithm that has a time-complexity that is linear in the number of users.