Efficient algorithm for calculating distance between a community (interconnected nodes) to another point

Question

I have a graph structure in a spatial domain (say a dense community like structure) and a query point. I want to devise efficient algorithms + Data Structures to calculate distance between this group as a whole and the query point.

A suitable distance function here could be averaging the distance of all points from the query point. An alternative function could be taking the maximum of all distances.

How should I go about this problem?

I'd recommended pre-computing the centroid of your community and just measuring distance to an arbitrary point via the centroid. — ProgrammerDan, Apr 22 '14 at 16:41
How does this question relate to the [tag:rtree]? You seem to already have the neighbors. — Has QUIT--Anony-Mousse, Apr 22 '14 at 17:55
I think designing an efficient solution for this problem will need some form of spatial indexing (which R-Trees are good at) — Nitish Upreti, Apr 23 '14 at 00:46

score 2 · Accepted Answer · answered Apr 22 '14 at 17:00

If spatial distances: I would suggest root-mean-square distance, which, unlike centroid, is in the spirit of your two suggestions in that it is a function of the distances from the query point to each point in the community. Preprocess the community by summing, for each point (x, y), the distance squared polynomial (X - x)^2 + (Y - y)^2 in variable X and Y. Then compute the RMS distance by plugging in the query point, dividing by the number of community points, and taking the square root.

Efficient algorithm for calculating distance between a community (interconnected nodes) to another point

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