## Abstract

The problem of finding the period of a vector V is central to many applications. Let V′ be a periodic vector closest to V under some metric. We seek this V′, or more precisely we seek the smallest period that generates V′. In this paper we consider the problem of finding the closest periodic vector in L _{p} spaces. The measures of "closeness" that we consider are the metrics in the different L _{p} spaces. Specifically, we consider the L _{1}, L _{2} and L _{∞} metrics. In particular, for a given n-dimensional vector V, we develop O(n ^{2}) time algorithms (a different algorithm for each metric) that construct the smallest period that defines such a periodic n-dimensional vector V′. We call that vector the closest periodic vector of V under the appropriate metric. We also show (three) O(n logn) time constant approximation algorithms for the (appropriate) period of the closest periodic vector.

Original language | English |
---|---|

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

Pages | 714-723 |

Number of pages | 10 |

DOIs | |

State | Published - 2011 |

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

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7074 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 |
---|---|

Country/Territory | Japan |

City | Yokohama |

Period | 5/12/11 → 8/12/11 |

## Fingerprint

Dive into the research topics of 'Closest periodic vectors in L_{p}spaces'. Together they form a unique fingerprint.