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.MFCS.2018.61
URN: urn:nbn:de:0030-drops-96431
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9643/
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Dixon, Peter ; Pavan, A. ; Vinodchandran, N. V.

On Pseudodeterministic Approximation Algorithms

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LIPIcs-MFCS-2018-61.pdf (0.4 MB)


Abstract

We investigate the notion of pseudodeterminstic approximation algorithms. A randomized approximation algorithm A for a function f is pseudodeterministic if for every input x there is a unique value v so that A(x) outputs v with high probability, and v is a good approximation of f(x). We show that designing a pseudodeterministic version of Stockmeyer's well known approximation algorithm for the NP-membership counting problem will yield a new circuit lower bound: if such an approximation algorithm exists, then for every k, there is a language in the complexity class ZPP^{NP}_{tt} that does not have n^k-size circuits. While we do not know how to design such an algorithm for the NP-membership counting problem, we show a general result that any randomized approximation algorithm for a counting problem can be transformed to an approximation algorithm that has a constant number of influential random bits. That is, for most settings of these influential bits, the approximation algorithm will be pseudodeterministic.

BibTeX - Entry

@InProceedings{dixon_et_al:LIPIcs:2018:9643,
  author =	{Peter Dixon and A. Pavan and N. V. Vinodchandran},
  title =	{{On Pseudodeterministic Approximation Algorithms}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{61:1--61:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9643},
  URN =		{urn:nbn:de:0030-drops-96431},
  doi =		{10.4230/LIPIcs.MFCS.2018.61},
  annote =	{Keywords: Approximation Algorithms, Circuit lower bounds, Pseudodeterminism}
}

Keywords: Approximation Algorithms, Circuit lower bounds, Pseudodeterminism
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018


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