Pathology of Traveling-Salesman Subtour-Elimination Algorithms

An underlying theory for the traveling-salesman problem is developed, pathological performance of some existing techniques are predicted, and two algorithms are presented, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.

Abstract

The traveling-salesman problem has been the target of a substantial number of computational algorithms over the last two decades. Reported computational experience with these algorithms varies widely; authors, however, have generally failed to explain this variation adequately, or to offer predictive theories for their approaches. This paper (a) develops an underlying theory for the problem, (b) predicts pathological performance of some existing techniques, and (c) presents two algorithms, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.