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On the Complexity of Numerical Analysis

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Abstract

We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSlp: Given a division-free straight-line program producing an integer N, decide whether N>0. We show that OrdSlp lies in the counting hierarchy, and combining our results with work of Tiwari, we show that the Euclidean Traveling Salesman Problem lies in the counting hierarchy -- the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE.




BibTeX - Entry

@InProceedings{allender_et_al:DagSemProc.06111.12,
  author =	{Allender, Eric and B\"{u}rgisser, Peter and Kjeldgaard-Pedersen, Johan and Miltersen, Peter Bro},
  title =	{{On the Complexity of Numerical Analysis}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2006/613},
  URN =		{urn:nbn:de:0030-drops-6130},
  doi =		{10.4230/DagSemProc.06111.12},
  annote =	{Keywords: Blum-Shub-Smale Model, Euclidean Traveling Salesman Problem, Counting Hierarchy}
}

Keywords: Blum-Shub-Smale Model, Euclidean Traveling Salesman Problem, Counting Hierarchy
Seminar: 06111 - Complexity of Boolean Functions
Issue date: 2006
Date of publication: 20.11.2006


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