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  Constructing Extended Formulations from Reflection Relations

Kaibel, V., & Pashkovich, K. (2011). Constructing Extended Formulations from Reflection Relations. In Integer Programming and Combinatoral Optimization (pp. 287-300).

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Kaibel, V.1, Author
Pashkovich, Kanstantsin1, 2, Author           
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1Otto-von-Guericke-Universität Magdeburg, External Organizations, ou_1738156              
2International Max Planck Research School (IMPRS), Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738143              

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 Abstract: There are many examples of optimization problems whose associated polyhedra can be described much nicer, and with way less inequalities, by projections of higher dimensional polyhedra than this would be possible in the original space. However, currently not many general tools to construct such extended formulations are available. In this paper, we develop a framework of polyhedral relations that generalizes inductive constructions of extended formulations via projections, and we particularly elaborate on the special case of reflection relations. The latter ones provide polynomial size extended formulations for several polytopes that can be constructed as convex hulls of the unions of (exponentially) many copies of an input polytope obtained via sequences of reflections at hyperplanes. We demonstrate the use of the framework by deriving small extended formulations for the G-permutahedra of all finite reflection groups G (generalizing both Goeman's extended formulation of the permutahedron of size O(n log n) and Ben-Tal and Nemirovski's extended formulation with O(k) inequalities for the regular 2^k-gon) and for Huffman-polytopes (the convex hulls of the weight-vectors of Huffman codes). © Springer, Part of Springer Science+Business Media [accessed 2014 January 31st]

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Language(s): eng - English
 Dates: 2011
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: eDoc: 569909
DOI: 10.1007/978-3-642-20807-2_23
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Title: Integer Programming and Combinatoral Optimization
Source Genre: Book
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 287 - 300 Identifier: -

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Title: Lecture Notes in Computer Science
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Pages: - Volume / Issue: 6655 Sequence Number: - Start / End Page: - Identifier: -