# Weak Algebraic Monge Arrays

1 ARCHI - Architecture
INRIA Rocquencourt
Abstract : An $n\times n$ matrix $C$ is called a {\em weak Monge\/} matrix iff $c_{ii}+c_{rs}\le c_{is}+c_{ri}$ for all $1\le i\le r,s\le n$. 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 higher dimensional weak Monge arrays and prove that higher dimensional axial assignment problems can be solved efficiently if the cost-structure is a higher dimensional weak Monge array. Additionally, the concept of weak Monge arrays is related to other Monge properties and extended in an algebraic framework. Finally, the problem of testing whether or not a given array can be permuted to become a weak Monge array is solved.
Keywords :
Type de document :
Rapport
[Research Report] RR-2501, INRIA. 1995
Domaine :

Littérature citée [2 références]

https://hal.inria.fr/inria-00074176
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 14:40:54
Dernière modification le : vendredi 16 septembre 2016 - 15:13:22
Document(s) archivé(s) le : mardi 12 avril 2011 - 15:41:41

### Identifiants

• HAL Id : inria-00074176, version 1

### Citation

Rüdiger Rudolf, Dominique Fortin. Weak Algebraic Monge Arrays. [Research Report] RR-2501, INRIA. 1995. 〈inria-00074176〉

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