Reduced error pruning of branching programs cannot be approximated to within a logarithmic factor

Authors:
Richard Nock;Tapio Elomaa;Matti Kääriäinen
Affiliations:
Département Scientifique Interfacultaire, Université des Antilles-Guyane, Campus de Schoelcher, BP 7209, 97275 Schoelcher, Martinique, France;Department of Computer Science, P.O. Box 26 (Teollisuuskatu 23), FIN-00014 University of Helsinki, Finland;Department of Computer Science, P.O. Box 26 (Teollisuuskatu 23), FIN-00014 University of Helsinki, Finland
Venue:
Information Processing Letters
Year:
2003

Citing 12
Cited 0

Simplifying decision trees

International Journal of Man-Machine Studies - Special Issue: Knowledge Acquisition for Knowledge-based Systems. Part 5
C4.5: programs for machine learning

C4.5: programs for machine learning
Learning &mgr;-branching programs with queries

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
An introduction to computational learning theory

An introduction to computational learning theory
On learning width two branching programs (extended abstract)

COLT '96 Proceedings of the ninth annual conference on Computational learning theory
A threshold of ln n for approximating set cover

Journal of the ACM (JACM)
Some optimal inapproximability results

Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
A Fast, Bottom-Up Decision Tree Pruning Algorithm with Near-Optimal Generalization

ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT

ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
The Difficulty of Reduced Error Pruning of Leveled Branching Programs

Annals of Mathematics and Artificial Intelligence
An analysis of reduced error pruning

Journal of Artificial Intelligence Research

Quantified Score

Hi-index	0.89

Visualization

Abstract

In this paper, we prove under a plausible complexity hypothesis that Reduced Error Pruning of branching programs is hard to approximate within log1-δ n, for every δ 0, where n is the number of description variables, a measure of the problem's complexity. The result holds under the assumption that NP problems do not admit deterministic, slightly superpolynomial time algorithms: NP ⊄ TIME(|I|O(loglog |I|)). This improves on a previous result that only had a small constant inapproximability ratio, and puts a fairly strong constraint on the efficiency of potential approximation algorithms. The result also holds for read-once and µ-branching programs.