A nearly-linear bound for chasing nested convex bodies

C. J. Argue, Sébastien Bubeck, Michael B. Cohen, Anupam Gupta, Yin Tat Lee

Research output: Contribution to conferencePaperpeer-review


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 Kt ⊂ Rd and must output a point xt ∈ Kt. 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 6d(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 languageEnglish (US)
Number of pages6
StatePublished - 2019
Event30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States
Duration: Jan 6 2019Jan 9 2019


Conference30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/TerritoryUnited States
CitySan Diego

ASJC Scopus subject areas

  • Software
  • General Mathematics


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