A graph theoretic approach to statistical data security
SIAM Journal on Computing
An analytical comparison of different formulations of the travelling sales man problem
Mathematical Programming: Series A and B
An alternate formulation of the symmetric traveling salesman problem and its properties
Discrete Applied Mathematics
A Suggested Computation for Maximal Multi-Commodity Network Flows
Management Science
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Classification of travelling salesman problem formulations
Operations Research Letters
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The multistage insertion formulation (MI) for the symmetric traveling salesman problem (STSP), gives rise to a combinatorial object called pedigree. Pedigrees are in one-to-one correspondence with Hamiltonian cycles. The convex hull of all the pedigrees of a problem instance is called the pedigree polytope. The MI polytope is as tight as the subtour elimination polytope when projected into its two-subscripted variable space. It is known that the complexity of solving a linear optimization problem over a polytope is polynomial if the membership problem of the polytope can be solved in polynomial time. Hence the study of membership problem of the pedigree polytope is important. A polynomially checkable necessary condition is given by Arthanari in [5]. This paper provides a counter example that shows the necessary condition is not sufficient.