Extended formulations, nonnegative factorizations, and randomized communication protocols
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10318087" target="_blank" >RIV/00216208:11320/15:10318087 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10107-014-0755-3" target="_blank" >http://dx.doi.org/10.1007/s10107-014-0755-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10107-014-0755-3" target="_blank" >10.1007/s10107-014-0755-3</a>
Alternative languages
Result language
angličtina
Original language name
Extended formulations, nonnegative factorizations, and randomized communication protocols
Original language description
An extended formulation of a polyhedron is a linear description of a polyhedron together with a linear map such that . These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis' factorization theorem (Yannakakis in J Comput Syst Sci 43(3):441-466, 1991) provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of equals thenonnegative rank of its slack matrix . Moreover, Yannakakis also shows that the nonnegative rank of is at most , where is the complexity of any deterministic protocol computing . In this paper, we show that the latter result can be strengthened when weallow protocols to be randomized. In particular, we prove that the base- logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Programming, Series B
ISSN
0025-5610
e-ISSN
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Volume of the periodical
153
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
20
Pages from-to
75-94
UT code for WoS article
000361473100006
EID of the result in the Scopus database
2-s2.0-84941997801