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Approximating CSPs requires sub-exponential size linear programs Meka, Raghu
Description
We show that linear programming relaxations need sub-exponential size to beat trivial random guessing for approximately satisfying constraint satisfaction problems. In fact, we show that for such problems sub-exponential size relaxations are as powerful as n^(Omega(1))-rounds of Sherali-Adams hierarchy. Previously, only super-polynomial (~ n^(Omega(log n)) bounds were known any CSP [CLRS13]. Our bounds are obtained by exploiting and extending the recent progress in communication complexity for "lifting" query lower bounds to communication problems. The core of our results is a new decomposition theorem for "high-entropy rectangles" into structurally nice distributions and may be of independent interest in communication complexity. Joint work with Pravesh Kothari and Prasad Raghavendra.
Item Metadata
Title |
Approximating CSPs requires sub-exponential size linear programs
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-09-06T15:33
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Description |
We show that linear programming relaxations need sub-exponential size to beat trivial random guessing for approximately satisfying constraint satisfaction problems. In fact, we show that for such problems sub-exponential size relaxations are as powerful as n^(Omega(1))-rounds of Sherali-Adams hierarchy. Previously, only super-polynomial (~ n^(Omega(log n)) bounds were known any CSP [CLRS13].
Our bounds are obtained by exploiting and extending the recent progress in communication complexity for "lifting" query lower bounds to communication problems. The core of our results is a new decomposition theorem for "high-entropy rectangles" into structurally nice distributions and may be of independent interest in communication complexity.
Joint work with Pravesh Kothari and Prasad Raghavendra.
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Extent |
32 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: UCLA
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Series | |
Date Available |
2017-03-08
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0343100
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International