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On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

Let A be an m × n binary matrix, t ∈,{1,… ,m} be a threshold, and ε > 0 be a positive parameter. We show that given a family of O(nε) maximal t-frequent column sets for A, it is NP-complete to decide whether A has any further maximal t-frequent sets, or not, even when the number of such additional maximal t-frequent column sets may be exponentially large. In contrast, all minimal t-infrequent sets of columns of A can be enumerated in incremental quasi-polynomial time. The proof of the latter result follows from the inequality α ≤ (m-t+1)β, where α and β are respectively the numbers of all maximal t-frequent and all minimal t-infrequent sets of columns of the matrix A. We also discuss the complexity of generating all closed t-frequent column sets for a given binary matrix.

This research is supported in part by the National Science Foundation (Grant IIS- 0118635), the Office of Naval Research (Grant N00014-92-J-1375), and Grants-in- Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology of Japan. Visits of the second author to Rutgers University were also supported by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science.

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Author information

Authors and Affiliations

  1. RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, 08854-8003, New Jersey

    E. Boros & V. Gurvich

  2. Department of Computer Science, Rutgers University, 110 Frelinghuysen RoadPiscataway, 08854-8019, New Jersey

    L. Khachiyan

  3. Division of Systems Science, Graduate School of Engineering Science, OsakaUniversity, 560-8531, Toyonaka, Osaka, Japan

    K. Makino

Authors
  1. E. Boros
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  2. V. Gurvich
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  3. L. Khachiyan
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  4. K. Makino
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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Boros, E., Gurvich, V., Khachiyan, L., Makino, K. (2002). On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_10

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  • DOI: https://doi.org/10.1007/3-540-45841-7_10

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