منابع مشابه
Balancing Unit Vectors
Theorem A. Let x1, . . . , x2k+1 be unit vectors in a normed plane. Then there exist signs ε1, . . . , ε2k+1 ∈ {±1} such that ‖ P 2k+1 i=1 εixi‖ ≤ 1. We use the method of proof of the above theorem to show the following point facility location result, generalizing Proposition 6.4 of Y. S. Kupitz and H. Martini (1997). Theorem B. Let p0, p1, . . . , pn be distinct points in a normed plane such t...
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For n > 0, d ≥ 0, n ≡ d( mod 2 ), let K(n , d) denote the minimal cardinality of afamily V of ±1 vectors of length n, such that for any ±1 vector u of length n there is av ∈ V such that v . u ≤ d, where v . u is the usual scalar product of v and u. Ageneralization of a very simple construction due to Knuth shows thatK(n , d) ≤ lcn /(d + 1 ) rc. A proof is given here that thi...
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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 pap...
متن کاملMPC Validation and Aggregation of Unit Vectors
When dealing with privatized data, it is important to be able to protect against malformed user inputs. This becomes difficult in MPC systems as each server should not contain enough information to know what values any user has submitted. In this paper, we implement an MPC technique to verify blinded user inputs are unit vectors. In addition, we introduce a BGW circuit which can securely aggreg...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2017
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-016-3635-z