Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Apriori Property and Breadth-First Search Algorithms

  • Bart GoethalsEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_23


Downward closure property; Levelwise search; Monotonicity property


Given a large database of sets of items, called transactions, the goal of frequent itemset mining is to find all subsets of items, called itemsets, occurring frequently in the database, i.e., occurring in a given minimum number of transactions.

The search space of all itemsets is exponential in the number of different items occurring in the database. Hence, the naive approach to generate and count the frequency of all itemsets over the database can not be achieved within reasonable time. Also, the given databases could be massive, containing millions of transactions, making frequency counting a tough problem in itself.

Therefore, numerous solutions have been proposed to perform a more directed search through the search space, almost all relying on the well known Apriori-property. These solutions can be divided into breadth-first search and depth-first search, of which the first is discussed here.


This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Agrawal R, Mannila H, Srikant R, Toivonen H, Verkamo A. Fast discovery of association rules. In: Fayyad U, Piatetsky-Shapiro G, Smyth P, Uthurusamy R, editors. Advances in knowledge discovery and data mining. Cambridge, MA: MIT; 1996. p. 307–28.Google Scholar
  2. 2.
    Bayardo J, Roberto J. Efficiently mining long patterns from databases. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1998. p. 85–93.Google Scholar
  3. 3.
    Bodon F. A fast apriori implementation. In: Proceedings of the ICDM Workshop on Frequent Itemset Mining Implementations; 2003.Google Scholar
  4. 4.
    Borgelt C, Kruse R. Induction of association rules: apriori implementation. In: Proceedings of the 15th Conference on Computational Statistics; 2002. p. 395–400.CrossRefGoogle Scholar
  5. 5.
    Boulicaut JF, Bykowski A, Rigotti C. Free-sets: a condensed representation of boolean data for the approximation of frequency queries. Data Min Knowl Discov. 2003;7(1):5–22.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bykowski A, Rigitti C. A condensed representation to find frequent patterns. In: Proceedings of the 20th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems; 2001. p. 267–73.Google Scholar
  7. 7.
    Calders T, Goethals B. Mining all non-derivable frequent itemsets. In: Principles of Data Mining and Knowledge Discovery, 6th European Conference; 2002. p. 74–85.zbMATHCrossRefGoogle Scholar
  8. 8.
    Calders T, Goethals B. Minimal k-free representations of frequent sets. In: Principles of Data Mining and Knowledge Discovery, 7th European Conference; 2003. p. 71–82.CrossRefGoogle Scholar
  9. 9.
    Gunopulos D, Khardon R, Mannila H, Saluja S, Toivonen H, Sharma R. Discovering all most specific sentences. ACM Trans Database Syst. 2003;28(2):140–74.CrossRefGoogle Scholar
  10. 10.
    Mannila H. Inductive databases and condensed representations for data mining. In: Proceedings of the 14th International Conference on Logic Programming; 1997. p. 21–30.Google Scholar
  11. 11.
    Pasquier N, Bastide Y, Taouil R, Lakhal L. Discovering frequent closed itemsets for association rules. In: Proceedings of the 7th International Conference on Database Theory; 1999. p. 398–416.Google Scholar
  12. 12.
    Savasere A, Omiecinski E, Navathe S. An efficient algorithm for mining association rules in large databases. In: Proceedings of the 21th International Conference on Very Large Data Bases; 1995. p. 432–44.Google Scholar
  13. 13.
    Toivonen H. Sampling large databases for association rules. In: Proceedings of the 22th International Conference on Very Large Data Bases; 1996. p. 134–45.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of AntwerpAntwerpBelgium

Section editors and affiliations

  • Jian Pei
    • 1
  1. 1.School of Computing ScienceSimon Fraser Univ.BurnabyCanada