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In this note, we consider an embedding of a Hamiltonian cycle problem in a Markov decision process (MDP). We propose a branch and bound type method based on the frequency polytope resulting from this embedding. Among the special features of the proposed scheme are the properties that: (i) a three-way branching is the biggest that can occur, (ii) no integer-valued variable is required, and (iii), the size of the LPs solved at the nodes of the branch and bound tree can only decrease as one moves down the tree. We hope that this note will encourage researchers in combinatorial optimization to experiment with the Markov decision process embedding as a basis for new algorithmic procedures.

A non-standard branch and bound method for the Hamiltonian cycle problem