Abstract
In 1971, Knuth gave an O(n2)-time algorithm for the classic problem of finding an optimal binary search tree. Knuth’s algorithm works only for search trees based on 3-way comparisons, but most modern computers support only 2-way comparisons (). Until this paper, the problem of finding an optimal search tree using 2- way comparisons remained open — poly-time algorithms were known only for restricted variants. We solve the general case, giving (i) an O(n4)-time algorithm and (ii) an O(n log n)-time additive-3 approximation algorithm. For finding optimal binary split trees, we (iii) obtain a linear speedup and (iv) prove some previous work incorrect.
Cite
CITATION STYLE
Chrobak, M., Golin, M., Ian Munro, J., & Young, N. E. (2015). Optimal search trees with 2-Way comparisons. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9472, pp. 71–82). Springer Verlag. https://doi.org/10.1007/978-3-662-48971-0_7
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