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Online Vector Balancing and Geometric Discrepancy
[article]

2020
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arXiv
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pre-print

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 small as possible. A concrete example is the online interval discrepancy problem where T points are sampled uniformly in [0,1], and the goal is to immediately color them ± such that every sub-interval remains nearly balanced. As random coloring incurs Ω(T^1/2) discrepancy, while the

arXiv:1912.03350v2
fatcat:f6qyelc2uzepdd63o3x4pp5mxm