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Lifting with Inner Functions of Polynomial Discrepancy

Authors Yahel Manor, Or Meir

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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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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

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.

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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