This project investigates the optimal placement of a server or multiple servers within a city of multiple users, in order to minimize the latency between each user and the server. In this project, I used Jupyter, Python, and NumPy as the general tools to find the solutions to the optimal placement.
The placement of one server can be formalized into a convex optimization problem, which was solved using both a cvxpy solver
and a manually implemented gradient descent algorithm. The code used can be viewed in the OneServer.ipynb file.
The placement of more servers is known to be a NP-hard non-convex integer program problem, which was approximated using a k-medians
approximation algorithm in the pyclustering package. The code used can be viewed in the FiveServers.ipybb file.
The theoretical mathematical background, methodology and other relevant information can be viewed in the report writeup at srp.pdf.