Statement

Given a connected network of N servers (numbered from 0 to N - 1, with 0 being the main server) connected by N - 1 cables, and you have a file that you want to serve. You can host your file on a server, and subsequently, all servers along the simple path from it to the main server will receive a copy of the file. The latency of a server V is defined as the minimum distance (number of cables) from V to a server that has a copy of your file. The network latency L is the maximum of all servers' latencies. Find the minimum achievable L if you can select at most K servers to host your file on (and each selected server will send a copy of the file to the servers on the simple path to the main server).