Algorithm to find the most adequate location compromise for several travellers

Question

I have been wondering for quite a while now if there was an already known algorithm solving the following problem or, at least, part of it.

Let's say there are a finite set of locations (x,y) and each of those locations have also a type (house, restaurant, café, cinéma...) and a weight (user rating, quality/price ratio ...). Moreover, there is a subset of paths faster than others (depending on the transportation type and the desired time of arrival).

The kind of question to answer: we are a group of people all located at n different locations, we wanna meet at time T, find us the best location (minimizing each's path length and travel time) of type t (cinema...).

Does that sound like any known algorithm?

Best regards, Rolf

Answer 1

There are several algorithms to solve this problem, this problem is known as Facility Location or k center problem http://en.wikipedia.org/wiki/Facility_location it's a NP Hard problem and there are some algorithms that aproximate solutions, also search for "Optimal meeting point" problem that it's used in spacial databases.