## Abstract

Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first non-trivial case when n=2. The most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes non-explicit schemes (existential results) for t≥3 using probabilistic arguments. We describe a fully explicit scheme for n=2 that matches their space bound of Θ(m ^{2/5}) bits for t=3 and, furthermore, improves upon it for t>3, answering their open problem. Our structure (consisting of query and storage algorithms) manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n≥3 that improve upon all previous fully explicit schemes for a wide range of parameters.

Original language | English |
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Title of host publication | Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 630-641 |

Number of pages | 12 |

ISBN (Print) | 9783662447765 |

DOIs | |

State | Published - 2014 |

Event | 22nd Annual European Symposium on Algorithms, ESA 2014 - Wroclaw, Poland Duration: 8 Sep 2014 → 10 Sep 2014 |

### 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 | 8737 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 22nd Annual European Symposium on Algorithms, ESA 2014 |
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Country/Territory | Poland |

City | Wroclaw |

Period | 8/09/14 → 10/09/14 |

### Bibliographical note

Funding Information:This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.

### Funding

This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.

Funders | Funder number |
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Natural Sciences and Engineering Research Council of Canada | |

Natural Sciences and Engineering Research Council of Canada | |

Canada Research Chairs |