Given a set of points in three-dimensional Cartesian space, I am looking for an algorithm that will sort these points in order to maximize the minimum Euclidean distance between two consecutive points.
It would also be useful if the algorithm maximized the average Euclidean distance between successive points.
Edit:
I crossed at https://cstheory.stackexchange.com/ and got a good answer. See https://cstheory.stackexchange.com/questions/8609/sorting-points-such-that-the-minimal-euclidean-distance-between-consecutive-poin .
Below is the lower bound on the cost of a solution, which can serve as a building block for a branch and a related or more unreliable incomplete search algorithm:
. http://en.wikipedia.org/wiki/Disjoint-set_data_structure, , . , , , . , , , , , .
, , , , NP-Hard, . wiki .
, , , node, 1/, ( ) NP-Hard. TSP.