A New Algorithm for the Construction of Optimal B-Trees

In this paper the construction of optimal B-trees for n keys, n key weights, and n+1 gap weights, is investigated. The best algorithms up to now have running time O(k n log n), where k is the order of the B-tree. These algorithms are based on dynamic programming and use step by step construction of larger trees from optimal smaller trees. We present a new algorithm, which has running time O(k nα), with α = 2 + log 2/ log(k + 1). This is a substantial improvement to the former algorithms. The improvement is achieved by applying a different dynamic programming paradigm. Instead of step by step construction from smaller subtrees a decision model is used, where the keys are placed by a sequential decision process in such a way into the tree, that the costs become optimal and the B-tree constraints are valid. CR Classification: E.1, H.2.2, I.2.8