Chasing Convex Bodies with Linear Competitive Ratio

C. J. Argue; Anupam Gupta; Guru Guruganesh; Ziye Tang

Chasing Convex Bodies with Linear Competitive Ratio

Data Structures and Algorithms 2020-01-08 v2 Metric Geometry

Authors: C. J. Argue , Anupam Gupta , Guru Guruganesh , Ziye Tang

Abstract

We study the problem of chasing convex bodies online: given a sequence of convex bodies $K_t\subseteq \mathbb{R}^d$ the algorithm must respond with points $x_t\in K_t$ in an online fashion (i.e., $x_t$ is chosen before $K_{t+1}$ is revealed). The objective is to minimize the sum of distances between successive points in this sequence. Bubeck et al. (STOC 2019) gave a $2^{O(d)}$ -competitive algorithm for this problem. We give an algorithm that is $O(\min(d, \sqrt{d \log T}))$ -competitive for any sequence of length $T$ .

Keywords

online algorithm approximation algorithm graph algorithm

Cite

@article{arxiv.1905.11877,
  title  = {Chasing Convex Bodies with Linear Competitive Ratio},
  author = {C. J. Argue and Anupam Gupta and Guru Guruganesh and Ziye Tang},
  journal= {arXiv preprint arXiv:1905.11877},
  year   = {2020}
}

Chasing Convex Bodies with Linear Competitive Ratio

Abstract

Keywords

Cite

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