  The box-constrained integer least squares problem (BILS) arises in MIMO
wireless communications applications. Typically a sphere decoding algorithm (a
tree search algorithm) is used to solve the problem. In order to make the
search algorithm more efficient, the columns of the channel matrix in the BILS
problem have to be reordered. To our knowledge, there are currently two
algorithms for column reordering that provide the best known results. Both use
all available information, but they were derived respectively from geometric
and algebraic points of view and look different. In this paper we modify one to
make it more computationally efficient and easier to comprehend. Then we prove
the modified one and the other actually give the same column reordering in
theory. Finally we propose a new mathematically equivalent algorithm, which is
more computationally efficient and is still easy to understand.
