Of course it can, but likely you will also need some search as well.
In math programming, we create a relaxation of the assignment problem where all of the integer decisions are converted to continuous. Then you solve this super simple Linear Program. This is a theoretical lower bound on what the optimal assignment is. You can now start branch and bound search and find the optimal integer assignment.
Now the trick is that we have identified over the decades cuts (inequalities) that you can apply to this initial relaxed problem, that they chop off irrelevant continuous space but let the integer solutions are untouched. If your cuts are good enough and the integer optimal solution is at the vertex of the chopped polytope, congratulations! You don't have to search anything!
In math programming, we create a relaxation of the assignment problem where all of the integer decisions are converted to continuous. Then you solve this super simple Linear Program. This is a theoretical lower bound on what the optimal assignment is. You can now start branch and bound search and find the optimal integer assignment.
Now the trick is that we have identified over the decades cuts (inequalities) that you can apply to this initial relaxed problem, that they chop off irrelevant continuous space but let the integer solutions are untouched. If your cuts are good enough and the integer optimal solution is at the vertex of the chopped polytope, congratulations! You don't have to search anything!