I'm interested in studying the problem of the optimal meeting point, which can be described as follow: $n$ individuals who want to gather in a restaurant (for example). They want a fair meeting point and to minimize the time/distance for everyone.
I'm looking for information on that problem, but I've only been able to find advanced paper on this problem.
- Is it part of a more general problem?
- Is graphs the best way to implement it? (the nodes are the possible meeting points, the edges are the possible roads for example..) How do current programs work, for example using maps like Google Map?
- Is it P or NP?
My difficulties to understand the problem and to find more informations about it
I know it's a bit vague, but I've got some difficulties because I don't know much about this kind of problems. I was just wondering one day "how to find the best restaurant in terms of distance to meet with some friends". I don't know what is mathematically the parameter that I should minimize to be "fair" (the sum of the distances of the $n$ individuals to the meeting point? The average?...).
Response to comment: (assuming that using graph is the best way to do it)
In input, we have a graph and we have the $n$ individuals (a list of $n$ vertices if we implement it with graphs, even if it means to add them to the graph), and in output, we get the optimal meeting point (i.e. the vertex which is at the minimal distance from all the $n$ individuals).