Find a route to visit all the points by nearest neighbour

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I have a 3D point cloud, given a starting point, I want to build a route that visits all points exactly once by the following steps:

1, find the nearest point of the current point in unvisited points.

2, visit the nearest point and regard it as the current point

3, repeat 1-2 until all the points are visited.

Now I employ nanoflann to build kd-tree to find the nearest points and delete visited points. However, the delete function of nanoflann is a lazy one in which the visited points are not really removed, leading to bad performance. Is there a better way to achieve such a route? or is there an ANN algorithm supporting deletion?

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