Initial Ideals of Toric Ideals and Group Relaxations in Integer Programming
by Serkan Hosten

Group relaxations provide an algebraic relaxation method to solve integer
programs where the condition on non-negativity of some integral variables is
relaxed. The set of such relaxation variables for a fixed cost vector is
closely related to the primary decomposotion and associated primes of the
corresponding initial ideal of the underlying toric ideal. The structure of
these relaxations and the associated primes are best understood using
polyhedral techniques and we will introduce these ideas.  In particular, using
these techniques we will show that associated primes of initial ideals of toric
ideals come in saturated chains.