  The tree reconstruction problem is to find an embedded straight-line tree
that approximates a given cloud of unorganized points in $\mathbb{R}^m$ up to a
certain error. A practical solution to this problem will accelerate a discovery
of new colloidal products with desired physical properties such as viscosity.
We define the Approximate Skeleton of any finite point cloud $C$ in a Euclidean
space with theoretical guarantees. The Approximate Skeleton ASk$(C)$ always
belongs to a given offset of $C$, i.e. the maximum distance from $C$ to
ASk$(C)$ can be a given maximum error. The number of vertices in the
Approximate Skeleton is close to the minimum number in an optimal tree by
factor 2. The new Approximate Skeleton of any unorganized point cloud $C$ is
computed in a near linear time in the number of points in $C$. Finally, the
Approximate Skeleton outperforms past skeletonization algorithms on the size
and accuracy of reconstruction for a large dataset of real micelles and random
clouds.
