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Weak Monge arrays in higher dimensions

✍ Scribed by Dominique Fortin; Rüdiger Rudolf

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
797 KB
Volume
189
Category
Article
ISSN
0012-365X

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✦ Synopsis

An n x n matrix C is called a weak Mange matrix if cii + c,~ GIs + cti for all 1 < i < r, s 6 n.

It is well known that the classical linear assignment problem is optimally solved by the identity permutation if the underlying cost-matrix fulfills the weak Monge property.

In this paper we introduce d-dimensional weak Monge arrays, (d >2), and prove that ddimensional axial assignment problems can be solved efficiently whenever the underlying costarray fulfills the d-dimensional weak Monge property. Moreover, it is shown that all results also carry over into an abstract algebraic framework. Finally, the problem of testing whether or not a given array can be permuted to become a weak Monge array is investigated.

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