On-Line Balancing of Random Inputs

Nikhil Bansal; Joel H. Spencer

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arXiv · 1903.06898

On-Line Balancing of Random Inputs

Nikhil Bansal·Joel H. Spencer

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Abstract

We consider an online vector balancing game where vectors $v_t$, chosen uniformly at random in $\{-1,+1\}^n$, arrive over time and a sign $x_t \in \{-1,+1\}$ must be picked immediately upon the arrival of $v_t$. The goal is to minimize the $L^\infty$ norm of the signed sum $\sum_t x_t v_t$. We give an online strategy for picking the signs $x_t$ that has value $O(n^{1/2})$ with high probability. Up to constants, this is the best possible even when the vectors are given in advance.

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Nikhil Bansal, Joel H. Spencer. 2020-07-12. On-Line Balancing of Random Inputs. https://arxiv.org/abs/1903.06898

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