Joint mixability of some integer matrices

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dc.citation.epage104en_US
dc.citation.spage90en_US
dc.citation.volumeNumber20en_US
dc.contributor.authorBellini, F.en_US
dc.contributor.authorKaraşan, O. E.en_US
dc.contributor.authorPınar, M. Ç.en_US
dc.date.accessioned2018-04-12T13:45:01Zen_US
dc.date.available2018-04-12T13:45:01Zen_US
dc.date.issued2016en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row sum the matrix has been termed jointly mixable (see e.g. Haus (2015), Wang and Wang (2015), Wang et al. (2013)). We show that the lack of joint mixability (the joint mixability gap) is not significant, i.e., the gap between the minimum maximal row sum and the maximum minimal row sum is either zero or one for a class of integer matrices including binary and complete consecutive integers matrices. For integer matrices where all entries are drawn from a given set of discrete values, we show that the gap can be as large as the difference between the maximal and minimal elements of the discrete set. The aforementioned result also leads to a polynomial-time approximation algorithm for matrices with restricted domain. Computing the gap for a {0,1,2}-matrix is proved to be equivalent to finding column permutations minimizing the difference between the maximum and minimum row sums. A polynomial procedure for computing the optimum difference by solving the maximum flow problem on an appropriate graph is given. © 2016 Elsevier B.V. All rights reserved.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T13:45:01Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2016en_US
dc.identifier.doi10.1016/j.disopt.2016.03.003en_US
dc.identifier.issn1572-5286en_US
dc.identifier.urihttp://hdl.handle.net/11693/38124en_US
dc.language.isoEnglishen_US
dc.publisherElsevier B.V.en_US
dc.publisherElsevier BVen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.disopt.2016.03.003en_US
dc.source.titleDiscrete Optimizationen_US
dc.subjectColumn permutationen_US
dc.subjectJointly mixable matricesen_US
dc.subjectMinimax row sumen_US
dc.subjectQuantilesen_US
dc.subjectApproximation algorithmsen_US
dc.subjectComputation theoryen_US
dc.subjectFlow graphsen_US
dc.subjectPolynomial approximationen_US
dc.subjectProbabilityen_US
dc.subjectRandom variablesen_US
dc.subjectColumn permutationsen_US
dc.subjectConsecutive integersen_US
dc.subjectDependence structuresen_US
dc.subjectMaximum flow problemsen_US
dc.subjectMinimaxen_US
dc.subjectPolynomial time approximation algorithmsen_US
dc.subjectProbability theoryen_US
dc.subjectQuantilesen_US
dc.subjectMatrix algebraen_US
dc.titleJoint mixability of some integer matricesen_US
dc.typeReviewen_US

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