An example to demonstrate the importance of using ellipsoidal norm in lattice basis reduction for branching on hyperplane algorithms
Zhifeng Li, Sanjay Mehrotra · 2009
The use of lattice basis reduction has been proposed in reformulating instances of hard integer programs. We construct integer programming instances showing that branching on hyperplane algorithms may benefit from using the geometrical information on the feasible set while using lattice basis reduction methods. Feasible as well as infeasible instances of these problems in four dimensions are given.