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  Balanced partitions of vector sequences

Bárány, I., & Doerr, B. (2006). Balanced partitions of vector sequences. Linear Algebra and its Applications, 414, 464-469.

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Bárány, Imre, Author
Doerr, Benjamin1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Let and  ·  be any norm on . Let B denote the unit ball with respect to this norm. We show that any sequence v1, v2, … of vectors in B can be partitioned into r subsequences V1, …, Vr in a balanced manner with respect to the partial sums: For all , we have . A similar bound holds for partitioning sequences of vector sets. Both results extend an earlier one of Bárány and Grinberg [I. Bárány, V.S. Grinberg, On some combinatorial questions in finite-dimensional spaces, Linear Algebra Appl. 41 (1981) 1–9] to partitions in arbitrarily many classes.

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Language(s): eng - English
 Dates: 2007-02-012006
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: eDoc: 314530
Other: Local-ID: C1256428004B93B8-7864B45F433AE0ACC125722E005C368D-Mcbg2006
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Title: Linear Algebra and its Applications
Source Genre: Journal
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Pages: - Volume / Issue: 414 Sequence Number: - Start / End Page: 464 - 469 Identifier: ISSN: 0024-3795