NDLI: Applications of Ramsey's theorem to decision tree complexity

Content Provider	ACM Digital Library
Author	Moran, Shlomo Snir, Marc Manber, Udi
Copyright Year	1985
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.
Starting Page	938
Ending Page	949
Page Count	12
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/4221.4259
Journal	Journal of the ACM (JACM)
Volume Number	32
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1985-10-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Decision tree reduction

The complexity of restricted spanning tree problems

The Tree-to-Tree Correction Problem

Propositional proof complexity

Complexity of Partial Satisfaction

Complexity of network synchronization

Separation of complexity classes

Theorem Proving with Lemmas

An optimal minimum spanning tree algorithm

Applications of Ramsey's theorem to decision tree complexity

Similar Documents

Decision tree reduction

The complexity of restricted spanning tree problems

The Tree-to-Tree Correction Problem

Propositional proof complexity

Complexity of Partial Satisfaction

Complexity of network synchronization

Separation of complexity classes

Theorem Proving with Lemmas

An optimal minimum spanning tree algorithm

Applications of Ramsey's theorem to decision tree complexity