License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ITCS.2017.11
URN: urn:nbn:de:0030-drops-81443
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Abboud, Amir ; Backurs, Arturs

Towards Hardness of Approximation for Polynomial Time Problems

LIPIcs-ITCS-2017-11.pdf (0.6 MB)


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

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-81443},
  doi =		{10.4230/LIPIcs.ITCS.2017.11},
  annote =	{Keywords: LCS, Edit Distance, Hardness in P}

Keywords: LCS, Edit Distance, Hardness in P
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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