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arXiv · 1610.05221

Balancing sums of random vectors

Juhan Aru·Bhargav Narayanan·Alex Scott·Ramarathnam Venkatesan
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Abstract

We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this paper, is closely related to the classical problem of partitioning a sequence of vectors into balanced subsequences, in addition to having applications to some problems in computer science.

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Juhan Aru, Bhargav Narayanan, Alex Scott, Ramarathnam Venkatesan. 2016-10-17. Balancing sums of random vectors. https://arxiv.org/abs/1610.05221

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