Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Efficient Construction of Near-Optimal Binary and Multiway Search Trees
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Performance guarantees for B-trees with different-sized atomic keys
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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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 n3 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.