  We present a linear programming based algorithm for computing a spanning tree
$T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is
$O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any
spanning tree of $P$. This is the first guaranteed approximation algorithm for
this problem. We provide a similar approximation algorithm for the more general
settings of building a spanning tree for a set system with bounded \VC
dimension. Our approach is an alternative to the reweighting technique
previously used in computing such spanning trees.
  Our approach is an alternative to the reweighting technique previously used
in computing such spanning trees.
