## Compressed Communication Complexity of Longest Common Prefixes

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings – Annual report year: 2018 › Research › peer-review

We consider the communication complexity of fundamental longest common prefix $$({{\mathrm{\textsc {Lcp}}}})$$ problems. In the simplest version, two parties, Alice and Bob, each hold a string, A and B, and we want to determine the length of their longest common prefix $$\ell ={{\mathrm{\textsc {Lcp}}}}(A,B)$$ using as few rounds and bits of communication as possible. We show that if the longest common prefix of A and B is compressible, then we can significantly reduce the number of rounds compared to the optimal uncompressed protocol, while achieving the same (or fewer) bits of communication. Namely, if the longest common prefix has an LZ77 parse of z phrases, only $$O(\lg z)$$ rounds and $$O(\lg \ell )$$ total communication is necessary. We extend the result to the natural case when Bob holds a set of strings $$B_1, \ldots , B_k$$ , and the goal is to find the length of the maximal longest prefix shared by A and any of $$B_1, \ldots , B_k$$ . Here, we give a protocol with $$O(\log z)$$ rounds and $$O(\lg z \lg k + \lg \ell )$$ total communication. We present our result in the public-coin model of computation but by a standard technique our results generalize to the private-coin model. Furthermore, if we view the input strings as integers the problems are the greater-than problem and the predecessor problem.

Original language | English |
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Title of host publication | String Processing and Information Retrieval |

Publisher | Springer |

Publication date | 2018 |

Pages | 74-87 |

ISBN (Print) | 9783030004798 |

DOIs | |

Publication status | Published - 2018 |

Event | 25th International Symposium on String Processing and Information Retrieval - Lima, Peru Duration: 9 Oct 2018 → 11 Oct 2018 |

### Conference

Conference | 25th International Symposium on String Processing and Information Retrieval |
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Country | Peru |

City | Lima |

Period | 09/10/2018 → 11/10/2018 |

Series | Lecture Notes in Computer Science |
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Volume | 11147 |

ISSN | 0302-9743 |

Citations | Web of Science® Times Cited: No match on DOI |
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- Communication complexity, LZ77, Compression Upper bound, Output sensitive , Longest common prefix, Predecessor

### Research areas

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