I have a problem that's been bugging me, but I'm not sure what algorithm can solve it.
Alice has medicine that she needs to use as quickly as possible in case of an allergy attack. She wants to distribute $k$ number of medicines in caches throughout her house, but doesn't know what is the ideal distribution such that at any room (or node) in the house she would travel the least amount of distance.
For simplicity, we map her house into an undirected graph where the edges represent distance to travel from one node (representing a room) to another node. The nodes and edges cannot be altered, and are static.
For $0 < k < |V|$, what algorithm can determine the ideal placement of medicines such that the Alice travels least amount of distance possible from any room (node) as starting point?