The dominance assignment problem

We prove the following remarkable fact for matrices with entries from an ordered set: For any m×n matrix A and a given integer h≤min{m,n} there exists a matrix C=(cij), obtained from A by permuting its rows and columns, such that cm−h+i,i≤cjk for j≤m−h+i and i≤k. Moreover, we give a polynomial algor...

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Bibliographic Details
Published inDiscrete optimization Vol. 9; no. 3; pp. 149 - 158
Main Authors Calvillo, Gilberto, Romero, David
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2012
Subjects
Assignment problem
Bottleneck assignment
Clutter
Combinatorial matrices
Lexicographic bottleneck assignment
Permutations
Permutations
Combinatorial matrices
Assignment problem
65F30
05C85
Lexicographic bottleneck assignment
90B80
90C27
05A05
Bottleneck assignment
Clutter
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Summary:We prove the following remarkable fact for matrices with entries from an ordered set: For any m×n matrix A and a given integer h≤min{m,n} there exists a matrix C=(cij), obtained from A by permuting its rows and columns, such that cm−h+i,i≤cjk for j≤m−h+i and i≤k. Moreover, we give a polynomial algorithm to transform A into C. We also prove that when h=m=n and all entries of A are distinct, the diagonal of C solves the lexicographic bottleneck assignment problem, and that the given algorithm has complexity O(n3n/logn), which is the best performance known for this kind of matrices.
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2012.06.001