A genuinely polynomial primal simplex algorithm for the assignment problem

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dc.citation.epage115en_US
dc.citation.issueNumber2en_US
dc.citation.spage93en_US
dc.citation.volumeNumber45en_US
dc.contributor.authorAkgül, M.en_US
dc.date.accessioned2016-02-08T10:54:05Z
dc.date.available2016-02-08T10:54:05Zen_US
dc.date.issued1993en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe present a primal simplex algorithm that solves the assignment problem in 1 2n(n+3)-4 pivots. Starting with a problem of size 1, we sequentially solve problems of size 2,3,4,...,n. The algorithm utilizes degeneracy by working with strongly feasible trees and employs Dantzig's rule for entering edges for the subproblem. The number of nondegenerate simplex pivots is bounded by n-1. The number of consecutive degenerate simplex pivots is bounded by 1 2(n-2)(n+1). All three bounds are sharp. The algorithm can be implemented to run in O(n3) time for dense graphs. For sparse graphs, using state of the art data structures, it runs in O(n2 log n+nm) time, where the bipartite graph has 2n nodes and m edges. © 1993.en_US
dc.identifier.doi10.1016/0166-218X(93)90054-Ren_US
dc.identifier.eissn1872-6771
dc.identifier.issn0166-218X
dc.identifier.urihttp://hdl.handle.net/11693/26037en_US
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/0166-218X(93)90054-Ren_US
dc.source.titleDiscrete Applied Mathematicsen_US
dc.subjectAssignment problemen_US
dc.subjectHirsch conjectureen_US
dc.subjectLinear programmingen_US
dc.subjectNetwork simplex methoden_US
dc.subjectPolynomial algorithmsen_US
dc.subjectStrongly feasible basesen_US
dc.titleA genuinely polynomial primal simplex algorithm for the assignment problemen_US
dc.typeArticleen_US

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