The Northwest corner rule revisited

Under which conditions can one permute the rows and columns in an instance of the transportation problem, such that the Northwest corner rule solves the resulting permuted instance to optimality? And under which conditions will the Northwest corner rule find the optimal solution for every possible p...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 159; no. 12; pp. 1284 - 1289
Main Authors Klinz, Bettina, Woeginger, Gerhard J.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.07.2011
Elsevier
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Basic feasible solution
Calculus of variations and optimal control
Combinatorics
Combinatorics. Ordered structures
Computational complexity
Computer science; control theory; systems
Corners
Exact sciences and technology
Mathematical analysis
Mathematics
Northwest
Optimization
Permutations
Sciences and techniques of general use
Sum matrix
Theoretical computing
Touch
Transportation problem
Transportation problem
Computational complexity
Sum matrix
Basic feasible solution
Area
Computer theory
Permutation
Optimal solution
Combinatorics
Optimization
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Summary:Under which conditions can one permute the rows and columns in an instance of the transportation problem, such that the Northwest corner rule solves the resulting permuted instance to optimality? And under which conditions will the Northwest corner rule find the optimal solution for every possible permutation of the instance? We show that the first question touches the area of NP-completeness, and we answer the second question by a simple characterization of such instances.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.04.007