Lifting with Inner Functions of Polynomial Discrepancy

Yahel Manor; Or Meir

doi:10.4230/LIPIcs.APPROX/RANDOM.2022.26

Lifting with Inner Functions of Polynomial Discrepancy

Yahel Manor, Or Meir

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Lifting theorems are theorems that bound the communication complexity of a composed function fogⁿ 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.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022
Editors	Amit Chakrabarti, Chaitanya Swamy
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772495
DOIs	https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.26
State	Published - 1 Sep 2022
Event	25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022 - Virtual, Urbana-Champaign, United States Duration: 19 Sep 2022 → 21 Sep 2022

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	245
ISSN (Print)	1868-8969

Conference

Conference	25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022
Country/Territory	United States
City	Virtual, Urbana-Champaign
Period	19/09/22 → 21/09/22

Bibliographical note

Publisher Copyright:
© Yahel Manor and Or Meir.

Keywords

Lifting
communication complexity
discrepancy
query complexity

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.APPROX/RANDOM.2022.26

Cite this

Manor, Y., & Meir, O. (2022). Lifting with Inner Functions of Polynomial Discrepancy. In A. Chakrabarti, & C. Swamy (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022 Article 26 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 245). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.26

Manor, Yahel ; Meir, Or. / Lifting with Inner Functions of Polynomial Discrepancy. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. editor / Amit Chakrabarti ; Chaitanya Swamy. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. (Leibniz International Proceedings in Informatics, LIPIcs).

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title = "Lifting with Inner Functions of Polynomial Discrepancy",

abstract = "Lifting theorems are theorems that bound the communication complexity of a composed function fogn 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.",

keywords = "Lifting, communication complexity, discrepancy, query complexity",

author = "Yahel Manor and Or Meir",

note = "Publisher Copyright: {\textcopyright} Yahel Manor and Or Meir.; 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022 ; Conference date: 19-09-2022 Through 21-09-2022",

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doi = "10.4230/LIPIcs.APPROX/RANDOM.2022.26",

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series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

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booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022",

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Manor, Y & Meir, O 2022, Lifting with Inner Functions of Polynomial Discrepancy. in A Chakrabarti & C Swamy (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022., 26, Leibniz International Proceedings in Informatics, LIPIcs, vol. 245, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022, Virtual, Urbana-Champaign, United States, 19/09/22. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.26

Lifting with Inner Functions of Polynomial Discrepancy. / Manor, Yahel; Meir, Or.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. ed. / Amit Chakrabarti; Chaitanya Swamy. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. 26 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 245).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Lifting with Inner Functions of Polynomial Discrepancy

AU - Manor, Yahel

AU - Meir, Or

PY - 2022/9/1

Y1 - 2022/9/1

N2 - Lifting theorems are theorems that bound the communication complexity of a composed function fogn 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.

AB - Lifting theorems are theorems that bound the communication complexity of a composed function fogn 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.

KW - Lifting

KW - communication complexity

KW - discrepancy

KW - query complexity

UR - https://www.scopus.com/pages/publications/85139113816

U2 - 10.4230/LIPIcs.APPROX/RANDOM.2022.26

DO - 10.4230/LIPIcs.APPROX/RANDOM.2022.26

M3 - Conference contribution

AN - SCOPUS:85139113816

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022

A2 - Chakrabarti, Amit

A2 - Swamy, Chaitanya

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022

Y2 - 19 September 2022 through 21 September 2022

ER -

Manor Y, Meir O. Lifting with Inner Functions of Polynomial Discrepancy. In Chakrabarti A, Swamy C, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2022. 26. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.APPROX/RANDOM.2022.26

Lifting with Inner Functions of Polynomial Discrepancy

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this