An algorithm for finding Hamilton cycles in random directed graphs
Journal of Algorithms
A parallel shortest augmenting path algorithm for the assignment problem
Journal of the ACM (JACM)
A parallel branch and bound algorithm for solving large asymmetric traveling salesman problems
Mathematical Programming: Series A and B
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The assignment problem is a well-known relaxation of the Asymmetric Traveling Salesman Problem (ATSP). Associated with every optimal dual solution to the assignment problem is a directed admissible graph. An ATSP solution is found if the admissible graph is Hamiltonian, otherwise the assignment problem bound may be strengthened. The exploitation of this result requires an exact algorithm for the directed Hamiltonian cycle problem. Computational results are presented for up to 3000 cities to show that determining the Hamiltonicity of admissible graphs improves the performance of an exact ATSP algorithm.