A new algorithm for the construction of optimal B-trees

Abstract

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 3 log n), where k is the order of the Btree. 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 n α), 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 decison 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.