License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.11
URN: urn:nbn:de:0030-drops-81443
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8144/
Abboud, Amir ;
Backurs, Arturs
Towards Hardness of Approximation for Polynomial Time Problems
Abstract
Proving hardness of approximation is a major challenge in the field of fine-grained complexity and conditional lower bounds in P.
How well can the Longest Common Subsequence (LCS) or the Edit Distance be approximated by an algorithm that runs in near-linear time?
In this paper, we make progress towards answering these questions.
We introduce a framework that exhibits barriers for truly subquadratic and deterministic algorithms with good approximation guarantees.
Our framework highlights a novel connection between deterministic approximation algorithms for natural problems in P and circuit lower bounds.
In particular, we discover a curious connection of the following form:
if there exists a \delta>0 such that for all \eps>0 there is a deterministic (1+\eps)-approximation algorithm for LCS on two sequences of length n over an alphabet of size n^{o(1)} that runs in O(n^{2-\delta}) time, then a certain plausible hypothesis is refuted, and the class E^NP does not have non-uniform linear size Valiant Series-Parallel circuits.
Thus, designing a "truly subquadratic PTAS" for LCS is as hard as resolving an old open question in complexity theory.
BibTeX - Entry
@InProceedings{abboud_et_al:LIPIcs:2017:8144,
author = {Amir Abboud and Arturs Backurs},
title = {{Towards Hardness of Approximation for Polynomial Time Problems}},
booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages = {11:1--11:26},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-029-3},
ISSN = {1868-8969},
year = {2017},
volume = {67},
editor = {Christos H. Papadimitriou},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8144},
URN = {urn:nbn:de:0030-drops-81443},
doi = {10.4230/LIPIcs.ITCS.2017.11},
annote = {Keywords: LCS, Edit Distance, Hardness in P}
}
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Keywords: |
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LCS, Edit Distance, Hardness in P |
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Collection: |
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8th Innovations in Theoretical Computer Science Conference (ITCS 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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28.11.2017 |
