## Abstract

Friedman and Linial [8] introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step t ∈ N, the online algorithm receives a request in the form of a convex body K_{t} ⊂ R^{d} and must output a point x_{t} ∈ K_{t}. The goal is to minimize the total movement between consecutive output points, where the distance is measured in some given norm. This problem is still far from being understood. Recently Bansal et al. [4] gave an 6^{d}(d!)^{2}-competitive algorithm for the nested version, where each convex body is contained within the previous one. We propose a different strategy which is O(dlog d)competitive algorithm for this nested convex body chasing problem. Our algorithm works for any norm. This result is almost tight, given an Ω(d) lower bound for the `_{∞} norm [8].

Original language | English (US) |
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Pages | 117-122 |

Number of pages | 6 |

DOIs | |

State | Published - 2019 |

Event | 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: Jan 6 2019 → Jan 9 2019 |

### Conference

Conference | 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 |
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Country/Territory | United States |

City | San Diego |

Period | 1/6/19 → 1/9/19 |

## ASJC Scopus subject areas

- Software
- General Mathematics