Lower bounds for algebraic decision trees

doi:10.1016/0196-6774(82)90002-5

Journal of Algorithms

Volume 3, Issue 1, March 1982, Pages 1-8

https://doi.org/10.1016/0196-6774(82)90002-5 Get rights and content

Abstract

A topological method is given for obtaining lower bounds for the height of algebraic decision trees. The method is applied to the knapsack problem where an $Ω(n^{2})$ bound is obtained for trees with bounded-degree polynomial tests, thus extending the Dobkin-Lipton result for linear trees. Applications to the convex hull problem and the distinct element problem are also indicated. Some open problems are discussed.

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^∗: The research of this author was supported in part by Office of Naval Research Contract N00014-76-C-0475 (NR-042-267).

^†: The research of this author was supported in part by National Science Foundation Grant MCS-77-05313-A01.

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Lower bounds for algebraic decision trees

Abstract

J. Comput. System Sci.

J. Comput. System Sci.

J. Comput. System Sci.

Real algebraic geometry (The 16th Hilbert problem)

Some Recollections from 30 Years Ago

On the complexity of varying sets of primitives

J. Comput. System Sci.

Foundations of Algebraic Topology