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 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 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.
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- 2.L. Gotlieb, “Optimal Multi-Way Search Trees,” SIAM Journal of Computing, vol. 10, no. 3, pp. 422–433, 1981.Google Scholar
- 3.Shou-Hsuan Stephen Huang and Venkatraman Viswanathan, “On the Construction of Weighted Time-Optimal B-Trees,” Bit, vol. 30, pp. 207–215, 1990.Google Scholar
- 5.K. Neumann and M. Morlock, Operations Research, Hanser, Munich, 1993.Google Scholar
- 6.J. Pearl, Heuristics — Intelligent Search Strategies for Computer Problem Solving, Addison-Wesley, 1984.Google Scholar
- 7.V. K. Vaishnavi, H. P. Kriegel, and D. Wood, “Optimum Multiway Search Trees,” Acta Informatica, vol. 14, pp. 119–133, 1980.Google Scholar