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dc.contributor.authorMurty, Katta G.en_US
dc.date.accessioned2006-09-11T19:32:21Z
dc.date.available2006-09-11T19:32:21Z
dc.date.issued1972-02en_US
dc.identifier.citationMurty, Katta G.; (1972). "A fundamental problem in linear inequalities with applications to the travelling salesman problem." Mathematical Programming 2(1): 296-308. <http://hdl.handle.net/2027.42/47908>en_US
dc.identifier.issn0025-5610en_US
dc.identifier.issn1436-4646en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/47908
dc.description.abstractWe consider a system of m linearly independent equality constraints in n nonnegative variables: Ax = b, x ≧ 0. The fundamental problem that we discuss is the following: suppose we are given a set of r linearly independent column vectors of A , known as the special column vectors. The problem is to develop an efficient algorithm to determine whether there exists a feasible basis which contains all the special column vectors as basic column vectors and to find such a basis if one exists. Such an algorithm has several applications in the area of mathematical programming. As an illustration, we show that the famous travelling salesman problem can be solved efficiently using this algorithm. Recent published work indicates that this algorithm has applications in integer linear programming. An algorithm for this problem using a set covering approach is described.en_US
dc.format.extent537785 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlag; The Mathematical Programming Societyen_US
dc.subject.otherCalculus of Variations and Optimal Controlen_US
dc.subject.otherMathematicsen_US
dc.subject.otherNumerical Analysisen_US
dc.subject.otherMathematics of Computingen_US
dc.subject.otherCombinatoricsen_US
dc.subject.otherOperation Research/Decision Theoryen_US
dc.subject.otherMathematical Methods in Physicsen_US
dc.subject.otherNumerical and Computational Methodsen_US
dc.subject.otherMathematical and Computational Physicsen_US
dc.subject.otherOptimizationen_US
dc.titleA fundamental problem in linear inequalities with applications to the travelling salesman problemen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumUniversity of Michigan, Ann Arbor, Michigan, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/47908/1/10107_2005_Article_BF01584550.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01584550en_US
dc.identifier.sourceMathematical Programmingen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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