On the hardness of the minimum height decision tree problem

Authors:
Eduardo S. Laber;Loana Tito Nogueira
Affiliations:
Departamento de Informática, PUC-Rio, Informatica, Rua Marques de Sao Vicente 225, R... 22453900 Rio de Janeiro, Brazil;Departamento de Informática, PUC-Rio, Informatica, Rua Marques de Sao Vicente 225, R... 22453900 Rio de Janeiro, Brazil
Venue:
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Year:
2004

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Abstract

Given a set of objects O and a set of tests T, the abstract decision tree problem (DTP) is to construct a tree with minimum height that completely identifies the objects of O, by using the tests of T. No algorithm with a good approximation ratio is known to solve this problem. We give a theoretical support for this fact by showing that DTP does not admit an o(log n)-approximation algorithm unless P = NP.