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Randomized complexity of linear arrangements and polyhedra?

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

We survey some of the recent results on the complexity of recognizing n-dimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive first nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming. We formulate further several open problems and possible directions for future research.

Article

Research partially supported by the DFG Grant KA 673/4-1, ESPRIT BR Grants 7079, 21726, and EC-US 030, by DIMACS, and by the Max-Planck Research Prize.

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Author information

Authors and Affiliations

  1. The Institute for Advanced Study, Princeton, and Dept. of Computer Science, University of Bonn, 53117, Bonn, USA

    Marek Karpinski

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  1. Marek Karpinski
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Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Karpinski, M. (1999). Randomized complexity of linear arrangements and polyhedra?. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_1

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  • DOI: https://doi.org/10.1007/3-540-48321-7_1

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  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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