dc.contributor.author Trevisan, Luca dc.contributor.author Xhafa Xhafa, Fatos dc.contributor.other Universitat Politècnica de Catalunya. Departament de Ciències de la Computació dc.date.accessioned 2016-02-18T14:20:05Z dc.date.available 2016-02-18T14:20:05Z dc.date.issued 1996-09 dc.identifier.citation Trevisan, L., Xhafa, F. "The Parallel complexity of positive linear programming". 1996. dc.identifier.uri http://hdl.handle.net/2117/83123 dc.description.abstract In this paper we study the parallel complexity of Positive Linear Programming (PLP), i.e. the special case of Linear Programming in packing/covering form where the input constraint matrix and constraint vector consist entirely of positive entries. We show that the problem of exactly solving PLP is P-complete. Luby and Nisan gave an NC approximation algorithm for PLP, and their algorithm can be used to approximate the size of the largest matching in bipartite graphs, or to approximate the size of the set cover to within a factor $(1+epsilon) ln Delta$, where $Delta$ is the maximum degree in the set system. Trevisan used positive linear programming in combination with Luby and Nisan's algorithm to obtain an NC $(3/4-epsilon)$-approximate algorithm for Max SAT. An important implication of our result is that, by using the Linear Programming technique, we cannot exactly compute in NC the cardinality of Maximum Matching in bipartite graphs or finding a $(ln Delta)$-approximation for Minimum Set Cover, or a 3/4-approximation of an instance of Maximum SAT, unless P=NC. dc.format.extent 5 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica dc.subject.other Positive linear programming dc.subject.other PLP dc.subject.other Complexity dc.title The Parallel complexity of positive linear programming dc.type External research report dc.rights.access Open Access local.identifier.drac 647399 dc.description.version Postprint (published version) local.citation.author Trevisan, L.; Xhafa, F.
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