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Lifting with Inner Functions of Polynomial Discrepancy

Authors Yahel Manor, Or Meir

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Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Oracles and decision trees
Keywords
  • Lifting
  • communication complexity
  • query complexity
  • discrepancy

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.26

Author Details

Yahel Manor
  • Department of Computer Science, University of Haifa, Israel
Or Meir
  • Department of Computer Science, University of Haifa, Israel

Funding

  • Manor, Yahel: Supported by the Israel Science Foundation (grant No. 716/20).
  • Meir, Or: Partially supported by the Israel Science Foundation (grant No. 716/20).

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