Distributed PCP Theorems for Hardness of Approximation in P
Name
1706.06407.pdf
Description
Submitted version
Size
385.21 KB
Format
Adobe PDF
Checksum (MD5)
9ce6af473cce22603d347bbe32ccb4ba
Author(s)
Abboud, Amir
Rubinstein, Aviad
Williams, Ryan
Date Issued
2017
Journal
Annual Symposium on Foundations of Computer Science - Proceedings
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Abboud, Amir, Rubinstein, Aviad and Williams, Ryan. 2017. "Distributed PCP Theorems for Hardness of Approximation in P." Annual Symposium on Foundations of Computer Science - Proceedings, 2017-October.
Version
Original manuscript
Abstract
© 2017 IEEE. We present a new distributed} model of probabilistically checkable proofs (PCP). A satisfying assignment x ∈{0,1}^n to a CNF formula φ is shared between two parties, where Alice knows x-1, \dots, x-{n/2, Bob knows x-{n/2+1},\dots,x-n, and both parties know φ. The goal is to have Alice and Bob jointly write a PCP that x satisfies φ, while exchanging little or no information. Unfortunately, this model as-is does not allow for nontrivial query complexity. Instead, we focus on a non-deterministic} variant, where the players are helped by Merlin, a third party who knows all of x.Using our framework, we obtain, for the first time, PCP-like reductions from the Strong Exponential Time Hypothesis (SETH) to approximation problems in \P. In particular, under SETH we show that %(assuming SETH) there are no truly-subquadratic approximation algorithms for %the following problems: Maximum Inner Product over \{0,1\}-vectors, LCS Closest Pair over permutations, Approximate Partial Match, Approximate Regular Expression Matching, and Diameter in Product Metric. All our inapproximability factors are nearly-tight. In particular, for the first three problems we obtain nearly-polynomial factors of 2^{(log n)^{1-o(1)}};only (1+o(1))-factor lower bounds (under SETH) were known before.As an additional feature of our reduction, we obtain new SETH lower bounds for the exact} monochromatic Closest Pair problem in the Euclidean, Manhattan, and Hamming metrics.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/FOCS.2017.12
