APPLICATIONS OF RAMSEY'S THEOREM TO DECISION TREES COMPLEXITY.

Shlomo Moran, Marc Snir, Udi Manber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Combinatorial techniques for extending lower bounds results for decision trees to general types of queries are presented. The authors consider problems, which they call order invariant, that are defined by simple inequalities between inputs. A decision tree is called k-bounded if each query depends on at most k variables. No further assumptions on the type of queries are made. It is proved that one can replace the queries of any k-bounded decision tree that solves an order invariant problem over a large enough input domain with 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 k-bounded decision trees, where k is a constant. Also proved is an OMEGA (n log n) lower bound for the element uniqueness problem and several other problems for any k-bounded decision tree, such that k equals O(n**c ) and c greater than 1/2. This lower bound is tight since there exist n**1 **/ **2 -bounded decision trees of complexity O(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.

Original languageEnglish (US)
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherIEEE
Pages332-337
Number of pages6
ISBN (Print)081860591X
StatePublished - Dec 1 1984
Externally publishedYes

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

ASJC Scopus subject areas

  • Hardware and Architecture

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