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Parameterized Inapproximability Hypothesis under Exponential Time Hypothesis

Authors:

Venkatesan Guruswami,

Kewen WuAuthors Info & Claims

STOC 2024: Proceedings of the 56th Annual ACM Symposium on Theory of Computing

Pages 24 - 35

https://doi.org/10.1145/3618260.3649771

Published: 11 June 2024 Publication History

Abstract

The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to satisfy an ε fraction of constraints for some absolute constant ε > 0. PIH plays the role of the PCP theorem in parameterized complexity. However, PIH has only been established under Gap-ETH, a very strong assumption with an inherent gap. In this work, we prove PIH under the Exponential Time Hypothesis (ETH). This is the first proof of PIH from a gap-free assumption. Our proof is self-contained and elementary. We identify an ETH-hard CSP whose variables take vector values, and constraints are either linear or of a special parallel structure. Both kinds of constraints can be checked with constant soundness via a “parallel PCP of proximity” based on the Walsh-Hadamard code.

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Cited By

Koch CStrassle CTan L(2024)Fast Decision Tree Learning Solves Hard Coding-Theoretic Problems2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00114(1893-1910)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00114
Bitansky NHarsha PIshai YRothblum RWu D(2024)Dot-Product Proofs and Their Applications2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00057(806-825)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00057

Index Terms

Parameterized Inapproximability Hypothesis under Exponential Time Hypothesis
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms
    1. Parameterized complexity and exact algorithms
      1. Fixed parameter tractability

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cover image ACM Conferences

STOC 2024: Proceedings of the 56th Annual ACM Symposium on Theory of Computing

June 2024

2049 pages

ISBN:9798400703836

DOI:10.1145/3618260

General Chairs:
Bojan Mohar
Simon Fraser University, Canada
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Igor Shinkar
Simon Fraser University, Canada
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Ryan O'Donnell
Carnegie Mellon University, USA

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Published: 11 June 2024

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Cited By

Koch CStrassle CTan L(2024)Fast Decision Tree Learning Solves Hard Coding-Theoretic Problems2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00114(1893-1910)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00114
Bitansky NHarsha PIshai YRothblum RWu D(2024)Dot-Product Proofs and Their Applications2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00057(806-825)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00057

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