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dc.contributor.authorBarvinok, Alexander I.en_US
dc.date.accessioned2006-09-11T19:33:44Z
dc.date.available2006-09-11T19:33:44Z
dc.date.issued1995-07en_US
dc.identifier.citationBarvinok, Alexander I.; (1995). "New algorithms for linear k -matroid intersection and matroid k -parity problems." Mathematical Programming 69 (1-3): 449-470. <http://hdl.handle.net/2027.42/47928>en_US
dc.identifier.issn0025-5610en_US
dc.identifier.issn1436-4646en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/47928
dc.description.abstractWe present algorithms for the k -Matroid Intersection Problem and for the Matroid k -Parity Problem when the matroids are represented over the field of rational numbers and k > 2. The computational complexity of the algorithms is linear in the cardinality and singly exponential in the rank of the matroids. As an application, we describe new polynomially solvable cases of the k -Dimensional Assignment Problem and of the k -Dimensional Matching Problem. The algorithms use some new identities in multilinear algebra including the generalized Binet—Cauchy formula and its analogue for the Pfaffian. These techniques extend known methods developed earlier for k = 2.en_US
dc.format.extent1281717 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlag; The Mathematical Programming Society, Inc.en_US
dc.subject.otherMathematical Methods in Physicsen_US
dc.subject.otherOptimizationen_US
dc.subject.otherCalculus of Variations and Optimal Controlen_US
dc.subject.otherMathematics of Computingen_US
dc.subject.otherMathematical and Computational Physicsen_US
dc.subject.otherNumerical Analysisen_US
dc.subject.otherMathematicsen_US
dc.subject.otherMatroid K -Parity Problemen_US
dc.subject.otherCombinatoricsen_US
dc.subject.otherHyperdeterminanten_US
dc.subject.otherK -Matroid Intersection Problemen_US
dc.subject.otherOperation Research/Decision Theoryen_US
dc.subject.otherNumerical and Computational Methodsen_US
dc.titleNew algorithms for linear k -matroid intersection and matroid k -parity problemsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Mathematics, University of Michigan, 48109-1003, Ann Arbor, MI, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/47928/1/10107_2005_Article_BF01585571.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01585571en_US
dc.identifier.sourceMathematical Programmingen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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