A New Polytope for Symmetric Traveling Salesman Problem

The classical polytope associated with the symmetric traveling salesman problem (STSP) is usually studied as embedded in the standard subtour elimination polytope. Several classes of facet defining inequalities of the STSP polytope are used in practical enumeration algorithms. In this paper we consider the basic objects called pedigrees which are in 1-1 correspondence with the tours. The convex hull of these pedigrees yields a new polytope, called the pedigree polytope. In this paper, we study the pedigree polytope as embedded in the MI-relaxation polytope introduced in an earlier work by the author. One of the interesting properties of these pedigree polytopes is that they can be defined in a recursive manner. This yields a sequence of flow problems and the feasibility of them is sufficient for the membership in the pedigree polytope under study. Other properties of the pedigree polytopes derived from these results and their consequences are studied.