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Author Moran, Shlomo ♦ Snir, Marc ♦ Manber, Udi
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1985
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Combinatorial techniques for extending lower bound results for decision trees to general types of queries are presented. Problems that are defined by simple inequalities between inputs, called order invariant problems, are considered. A decision tree is called $\textit{k-bounded}$ if each query depends on at most $\textit{k}$ variables. No further assumptions on the type of queries are made. It is proved that one can replace the queries of any $\textit{k}-bounded$ decision tree that solves an order-invariant problem over a large enough input domain with $\textit{k}-bounded$ queries whose outcome depends only on the relative order of the inputs. As a consequence, all existing lower bounds for comparison-based algorithms are valid for general $\textit{k}-bounded$ decision trees, where $\textit{k}$ is a constant.An $&OHgr;(\textit{n}$ log $\textit{n})$ lower bound for the element uniqueness problem and several other problems for any $\textit{k}-bounded$ decision tree, such that $\textit{k}$ = $\textit{O}(\textit{nc})$ and $\textit{c}$ < 1/2 is proved. This lower bound is tight since there exist $\textit{n}1/2-bounded$ decision trees of complexity $\textit{O}(\textit{n})$ that solve the element-uniqueness problem. All the lower bounds mentioned above are shown to hold for nondeterministic and probabilistic decision trees as well.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1985-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 32
Issue Number 4
Page Count 12
Starting Page 938
Ending Page 949

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Source: ACM Digital Library