### Abstract

Finding frequent items in a data stream is a fundamental problem; Given a threshold θ ε (0,1), find items appearing more than θ·N times in an input stream with length N. Karp, Shenker, Papadimiriou (2003) gave a simple deterministic online algorithm, which allows false positive outputs using memory of O(θ ^{-1} log N) bits, while they also gave a lower bound. Motivated by the theoretical bound of the space complexity, this paper proposes a simple randomized online algorithm using memory of O(θ ^{-2} log ^{2} θ ^{-1}+log log N) bits where parameters for approximation are hidden in the constant. Our algorithm is robust for memory overflow, compared with other naïve randomized algorithms, or deterministic algorithms using memory of O(logN) bits. We also give some randomized algorithms for approximate counting.

Original language | English |
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Title of host publication | Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings |

Pages | 514-523 |

Number of pages | 10 |

DOIs | |

Publication status | Published - Dec 26 2011 |

Event | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan Duration: Dec 5 2011 → Dec 8 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7074 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 |
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Country | Japan |

City | Yokohama |

Period | 12/5/11 → 12/8/11 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings*(pp. 514-523). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_53