License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.19
URN: urn:nbn:de:0030-drops-171415
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17141/
Göös, Mika ;
Jain, Siddhartha
Communication Complexity of Collision
Abstract
The Collision problem is to decide whether a given list of numbers (x_1,…,x_n) ∈ [n]ⁿ is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n^Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x_i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov (CCC 2021).
BibTeX - Entry
@InProceedings{goos_et_al:LIPIcs.APPROX/RANDOM.2022.19,
author = {G\"{o}\"{o}s, Mika and Jain, Siddhartha},
title = {{Communication Complexity of Collision}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
pages = {19:1--19:9},
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/opus/volltexte/2022/17141},
URN = {urn:nbn:de:0030-drops-171415},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.19},
annote = {Keywords: Collision, Communication complexity, Lifting}
}
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Keywords: |
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Collision, Communication complexity, Lifting |
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Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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15.09.2022 |
