22. The system of claim 21 , wherein the constraint process module further comprises an implication graph generation module configured to generate a Boolean implication graph based on the Boolean variables, the Boolean implication graph modeling a possible position of the layout object, and wherein the infeasibility determination module is configured to determine satisfiability of the Boolean implication graph to determine whether the set of layout constraints is infeasible.
21. A system for legalizing a circuit layout using a plurality of non-uniform grids, the circuit layout for manufacturing a circuit, the circuit layout comprised of a layout object, the system comprising: a constraint generation module configured to generate a set of layout constraints for the layout object based on the plurality of non-uniform grids, the set of layout constraints comprising design rule check constraints and gridding requirements, the gridding requirements being requisites for the layout object to align to one of the plurality of non-uniform grids, the layout object having layout variables to identify a position of the layout object; a constraint process module configured to process the set of layout constraints to a feasible form for the layout object to be modified to satisfy the set of layout constraints, the constraint process module comprising: a Boolean variable conversion module configured to assign Boolean variables to the layout variables, each Boolean variable from the Boolean variables assigned to a corresponding layout variable from the layout variables, an infeasibility determination module configured to determine whether the set of layout constraints is infeasible using the Boolean variables assigned to the layout variables, the infeasibility determination module further configured to identify an infeasible layout constraint from the set of layout constraints, responsive to the set of layout constraints determined to be infeasible, the infeasible layout constraint causing the set of layout constraints to be infeasible, and a constraint relaxation module configured to relax the identified infeasible layout constraint for the set of layout constraints to be in the feasible form, responsive to the set of layout constraints determined to be infeasible; and an output layout generator module configured to generate by solving the set of layout constraints in the feasible form with a linear program solver, an output circuit layout to provide for manufacture of the circuit.