When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.11
URN: urn:nbn:de:0030-drops-81443
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8144/
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### Towards Hardness of Approximation for Polynomial Time Problems

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### 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},