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Unique Sink Orientations of Grids

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Integer Programming and Combinatorial Optimization (IPCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3509))

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Abstract

We introduce unique sink orientations of grids as digraph models for many well-studied problems, including linear programming over products of simplices and generalized linear complementarity problems over P-matrices (PGLCP). We investigate the combinatorial structure of such orientations and develop randomized algorithms for finding the sink. We show that the orientations arising from PGLCP satisfy the combinatorial Holt-Klee condition known to hold for polytope digraphs, and we give the first expected linear-time algorithms for solving PGLCP with a fixed number of blocks.

The first and the third author acknowledge support from the Swiss Science Foundation (SNF), Project No. 200021-100316/1. Part of this research was done at the 2004 Barbados Undercurrent Workshop Polyhedra, Convex Geometry, and Optimization at Bellairs Research Institute, McGill University. For a full paper see [1].

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, CH-8092, Zürich, Switzerland

    Bernd Gärtner & Leo Rüst

  2. Department of Mathematical Sciences, George Mason University, MS 3F2, US-Fairfax, VA, 22030-4444, USA

    Walter D. Morris

Authors
  1. Bernd Gärtner
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  2. Walter D. Morris
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  3. Leo Rüst
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln,  

    Michael Jünger

  2. Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Volker Kaibel

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Gärtner, B., Morris, W.D., Rüst, L. (2005). Unique Sink Orientations of Grids. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_16

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  • DOI: https://doi.org/10.1007/11496915_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26199-5

  • Online ISBN: 978-3-540-32102-6

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