Online vector balancing and geometric discrepancy

  title={Online vector balancing and geometric discrepancy},
  author={Nikhil Bansal and Haotian Jiang and Sahil Singla and Makrand Sinha},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  • N. BansalHaotian Jiang Makrand Sinha
  • Published 6 December 2019
  • Mathematics, Computer Science
  • Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
We consider an online vector balancing question where T vectors, chosen from an arbitrary distribution over [−1,1] n , arrive one-by-one and must be immediately given a ± sign. The goal is to keep the discrepancy—the ℓ∞-norm of any signed prefix-sum—as small as possible. A concrete example of this question is the online interval discrepancy problem where T points are sampled one-by-one uniformly in the unit interval [0,1], and the goal is to immediately color them ± such that every sub-interval… 

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