An efficient algorithm for reducing clauses based on constraint satisfaction techniques

Jérôme Maloberti, Einoshin Suzuki

Research output: Contribution to journalConference article

3 Citations (Scopus)

Abstract

This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

Original languageEnglish
Pages (from-to)234-251
Number of pages18
JournalLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
Volume3194
Publication statusPublished - Jan 1 2004
Event14th International Conference ILP 2004: Inductive Logic Programming - Porto, Portugal
Duration: Sep 6 2004Sep 8 2004

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Constraint Satisfaction
Efficient Algorithms
Minimal Solution
Inductive Logic Programming
Inductive logic programming (ILP)
Exhaustive Search
Constraint satisfaction problems
Constraint Satisfaction Problem
Search Algorithm
Learning Algorithm
Learning algorithms
NP-complete problem
Computational complexity
Data storage equipment
Approximation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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AB - This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

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