Computing sandpile configurations using integer linear programming

Sandpile group or Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. It is well known that these recurrent configurations can be characterized as optimal solution certain non-linear optimization problems. We show graph correspond to solutions some integer linear programs. More precisely, we present two new programming models, one computes other order configuration. As an application, calculate identity configuration for cone regular cycle with n+1 vertices using Weak Duality Theorem in programming.