Before revision: \le \le \lceil \rceil  To round the fractional solution, in our main technical contribution, we describe a fast near-linear time implementation of swap-rounding in the spanning tree polytope of a graph.
After revision: \le \le \lceil (1+\epsilon)B\rceil To round the fractional solution, in our main technical contribution, we describe a fast near-linear time implementation of swap-rounding in the spanning tree polytope of a graph.