
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24October 26
ISBN: 081860591X
ASCII Text  x  
S. Moran, M. Snir, U. Manber, "Applications Of Ramsey's Theorem To Decision Trees Complexity," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 332337, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984.  
BibTex  x  
@article{ 10.1109/SFCS.1984.715933, author = {S. Moran and M. Snir and U. Manber}, title = {Applications Of Ramsey's Theorem To Decision Trees Complexity}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1984}, isbn = {081860591X}, pages = {332337}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1984.715933}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Applications Of Ramsey's Theorem To Decision Trees Complexity SN  081860591X SP332 EP337 A1  S. Moran, A1  M. Snir, A1  U. Manber, PY  1984 VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Combinatorial techniques for extending lower bounds results for decision trees to general types of queries are presented. We consider problems, which we call order invariant, that are defined by simple inequalities between inputs. A decision tree is called kbounded if each query depends on at most k variables. We make no further assumptions on the type of queries. We prove that we can replace the queries of any kbounded decision tree that solves an order invariant problem over a large enough input dornain with kbounded 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 kbounded decision trees, where k is a constant. We also prove an /spl Omega/(n log n) lower bound for the element uniqueness problem and several other problems for any kbounded decision tree, such that k  )(n/sup c/) and c < 1/2. This lower bound is tight since that there exist n/sup 1/2/bounded decision trees of complexity 0(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.
Citation:
S. Moran, M. Snir, U. Manber, "Applications Of Ramsey's Theorem To Decision Trees Complexity," focs, pp.332337, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
Usage of this product signifies your acceptance of the Terms of Use.