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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.26

Lifting with Inner Functions of Polynomial Discrepancy

Authors: Yahel Manor and Or Meir

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract

Lifting theorems are theorems that bound the communication complexity of a composed function f∘gⁿ in terms of the query complexity of f and the communication complexity of g. Such theorems constitute a powerful generalization of direct-sum theorems for g, and have seen numerous applications in recent years. We prove a new lifting theorem that works for every two functions f,g such that the discrepancy of g is at most inverse polynomial in the input length of f. Our result is a significant generalization of the known direct-sum theorem for discrepancy, and extends the range of inner functions g for which lifting theorems hold.

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Yahel Manor and Or Meir. Lifting with Inner Functions of Polynomial Discrepancy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{manor_et_al:LIPIcs.APPROX/RANDOM.2022.26,
  author =	{Manor, Yahel and Meir, Or},
  title =	{{Lifting with Inner Functions of Polynomial Discrepancy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.26},
  URN =		{urn:nbn:de:0030-drops-171486},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.26},
  annote =	{Keywords: Lifting, communication complexity, query complexity, discrepancy}
}

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Lifting with Inner Functions of Polynomial Discrepancy

Abstract

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