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 Author, Editor(s)
 Author(s): Fleischer, Rudolf dblp
 BibTeX cite key*: Fleischer_dectrees_1999

 Title
 Title*: Decision trees: old and new results

 Journal
 Journal Title*: Information and computation Journal's URL: Download URL for the article: Language: English

 Publisher

 Vol, No, pp, Date
 Volume*: 152 Number: Publishing Date: 1999 Pages*: 44-61 Number of VG Pages: 39 Page Start: Page End: Sequence Number: DOI:

 Note: (LaTeX) Abstract: In this paper, we prove two general lower bounds for algebraic decision trees which test membership in a set $S\subseteq R^n$ which is defined by linear inequalities. Let $rank(S)$ be the maximal dimension of a linear subspace contained in the closure of $S$ {in the Euclidean topology}. First we show that any decision tree for $S$ which uses products of linear functions (we call such functions {\em mlf-functions}) must have depth at least $n-rank(S)$. This solves an open question raised by A.C.~Yao and can be used to show that mlf-functions are not really more powerful than simple comparisons between the input variables when computing the largest $k$ out of $n$ elements. Yao proved this result in the special case when products of at most two linear functions are allowed. Out proof also shows that any decision tree for this problem must have exponential size. Using the same methods, we can give an alternative proof of Rabin's Theorem, namely that the depth of any decision tree for $S$ using arbitrary analytic functions is at least $n-rank(S)$. URL for the Abstract: Categories, Keywords: decision tree, lower bound HyperLinks / References / URLs: Copyright Message: Personal Comments: Download Access Level:

 Correlation
 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Algorithms and Complexity Group Audience: experts only Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat

BibTeX Entry:

@ARTICLE{Fleischer_dectrees_1999,
AUTHOR = {Fleischer, Rudolf},
TITLE = {Decision trees: old and new results},
JOURNAL = {Information and computation},