algorithm - Balanced spanning tree (T) from undirected graph -

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i have connected undirected graph. looking way construct balanced spanning tree (t) of graph

the specific balanced spanning tree, define follows:

  1. if root of tree r .all nodes divided levels.i.e nodes distance r (in t) j in level lj,etc.
  2. for each node w 1 can define sub-tree t_w of t,such w root.
  3. the goal define spanning tree in such way each level li,for every 2 nodes u , v in level li number of nodes in t_u , t_v maximally equivalent.

does can advice algorithm/s building such “relatively” balanced spanning tree?

thank in advance.

i not sure expression "maximally equivalent."

this problem may not have perfect solution, obvious thing how better can do?

this problem in generality seems np-complete. greedy approaches might result in constant approx algorithms, if lucky.


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