Guruswami, Venkatesan ;
Tao, Runzhou
Streaming Hardness of Unique Games
Abstract
We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by p, the alphabet size of the Unique Game, gives a trivial p-approximation that can be computed in O(log n) space. Meanwhile, with high probability, a sample of O~(n) constraints suffices to estimate the optimal value to (1+epsilon) accuracy. We prove that any single-pass streaming algorithm that achieves a (p-epsilon)-approximation requires Omega_epsilon(sqrt n) space. Our proof is via a reduction from lower bounds for a communication problem that is a p-ary variant of the Boolean Hidden Matching problem studied in the literature. Given the utility of Unique Games as a starting point for reduction to other optimization problems, our strong hardness for approximating Unique Games could lead to downstream hardness results for streaming approximability for other CSP-like problems.
BibTeX - Entry
@InProceedings{guruswami_et_al:LIPIcs:2019:11220,
author = {Venkatesan Guruswami and Runzhou Tao},
title = {{Streaming Hardness of Unique Games}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
pages = {5:1--5:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-125-2},
ISSN = {1868-8969},
year = {2019},
volume = {145},
editor = {Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11220},
URN = {urn:nbn:de:0030-drops-112209},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.5},
annote = {Keywords: Communication complexity, CSP, Fourier Analysis, Lower bounds, Streaming algorithms, Unique Games}
}
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Keywords: |
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Communication complexity, CSP, Fourier Analysis, Lower bounds, Streaming algorithms, Unique Games |
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Seminar: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
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Issue date: |
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2019 |
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Date of publication: |
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2019 |
2019
