Separating Simple Domino Parity Inequalities

In IPCO 2002, Letchford and Lodi describe an algorithm for separating simple comb inequalities that runs in O(nm log n) time, where n and m are respectively the number of nodes and arcs in the support graph of the point to be separated. In this extended abstract, we demonstrate that the above algorithm separates over a superclass of simple comb inequalities, which we call simple domino parity inequalities. We also prove several structural properties about the support graph of points in the subtour polytope. With these, we design a faster separation algorithm for simple domino parity inequalities. Our algorithm runs inO(nm log n 2 m ) time.