On an efficient dynamic programming technique of F. F. Yao

A very useful technique of F. F. Yao for providing efficient dynamic programming algorithms involves establishing the so called quadrangle inequalities on cost functions. A major application of this technique is in speeding up the classical dynamic programming algorithm for optimal binary search trees. We consider a generalization of the classical problem, which arises from considering search strategies on a sequential access file or tape. For this problem, Yao's quadrangle inequalities are not strong enough to lead to a speedup of the dynamic programming algorithm. Here, we extend the domain of efficient dynamic programming by establishing strong quadrangle inequalities which do imply a speedup.