To the Steinitz lemma in coordinate form
type: Item
instance of: scholarly article
title: To the Steinitz lemma in coordinate form
zbMATH Open document ID: 0881.68061
DOI: 10.1016/0012-365X(94)00240-J
author: Sergey Sevastyanov
author: Wojciech Banaszczyk
published in: Discrete Mathematics
publication date: 1997-08-26T00:00:00Z
review text: We consider an arbitrary finite family of vectors in \(m\)-dimensional space with sum zero and the absolute value of any vector's coordinate at most 1. We prove that there exists an order of vector summation for this family such that every partial sum has the absolute value of the first coordinate at most 1 while the other coordinates are bounded by a constant at most \(O(m^{3/2})\). We also describe a polynomial-time algorithm which computes an order of vector summation for which all partial sums meet somewhat weaker bounds (at most \(O(m^2)\)) on the absolute value of coordinates from 2 to \(m\). (The absolute value of the first coordinate still remains at most 1.).
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 52C99
zbMATH DE Number: 1021677
zbMATH Keywords: vector summation
zbMATH Keywords: Steinitz constant
zbMATH Keywords: polynomial-time algorithm
MaRDI profile type: Publication
Wikidata QID: Q124852352
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description: scientific article; zbMATH DE number 1021677