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doi:10.1016/j.ipl.2007.08.025 
Copyright © 2007 Elsevier B.V. All rights reserved.
The complexity of linear programming in (γ,κ)-form
Pavlos S. Efraimidisa, 
Received 15 May 2006;
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Abstract
Linear programming in (γ,κ)-form is a restricted class of linear programming (LP) introduced in [L. Trevisan, Parallel approximation algorithms by positive linear programming. Algorithmica 21 (1998) 72–88]. Since [L. Trevisan, Erratum: A correction to parallel approximation algorithms by positive linear programming. Algorithmica 27 (2000) 115–119] the complexity of (γ,κ)-form LP is an open problem. In this work, we show that LP in (γ,κ)-form is P-Complete to be approximated within any constant factor. An immediate consequence is that the extension of Positive Linear Programming (PLP) where the coefficients (matrix A) can have negative values is also P-Complete to be approximated within any constant factor.
Keywords: Computational complexity; Approximation algorithms; Analysis of algorithms
